An astonishing number of interactions between Kotetsu and Barnaby involves this. They meet in Episode 1, and by Episode 2 they're quarreling like an old married couple.
Their first meeting involves Barnaby catching Kotetsuin his arms. When it happens again in Episode 10, Barnaby even remarks that it's been a while since he carried Kotetsu like this and teases him about having gained weight. Word of God indicates that he did, in fact, register the slight weight change (despite Kotetsu now being in a different suit).
The Princess Carry makes its appearance once more in Episode 25, following which the two have a short conversation while Barnaby is still holding Kotetsu. The conversation implies that the only reason Barnaby returned to the Superhero scene was to stay by Kotetsu's side.
Barnaby can be quite Kuudere / Tsundere at times (switching between the two depending on his mood)—and while the kuu and tsun sides are the default modes that he usually exposes to everyone, Kotetsu is the only person he is ever shown being dere towards.
(From Kotetsu's interview with Hero Gossip): "I like a woman who scolds me when Iím slacking off but is kind when the times are tough. [...] But Bunny always scolds me, saying ďYou could have read the instructions yourself, you know"."
Not to mention how Kotetsu gave both of them silly nicknames when he first met them. The parallels become more pronounced in Episode 17, when Barnaby repeats some of Tomoe's words almost verbatim.
(Comment on Episode 17 in Hero TV Fan Book 2): "Barnaby's words on TV bring back memories of Tomoe, who said the same thing on her deathbed."
Episode 9; Kotetsu has an extended conversation with Barnaby, during which the latter worries about Kotetsu's injuries and reveals most of the details regarding his childhood trauma. This is also the first time we see a genuine, open smile from Barnaby.
Towards the end of Episode 13, when Barnaby calls him "Kotetsu" instead of the usual "Oji-san", Kotetsu's expression was pretty d'aww-worthy.
He later admits that this made him so happy he went out drinking in celebration.
In Episode 19, Barnaby is asked if there's anyone he aspires to be like. His answer is that there isn't, but there's one person who he feels he can't compare to, and his greatest wish is to be noticed by this person. You get no points for guessing who that is.
This episode is chock-full of it, with Kotetsu making a meal for Barnaby (which is described in HeroTV Fan Book 2 as "The rice packed with Kotetsu's love detonates!") and saying that he worries about him (and showing it); a scene involving a crying Barnaby looking up at Kotetsu and saying his name (in a dramatic way that resembles a scene straight out of a shoujo manga) while in a rather compromising position◊ that goes straight to Does This Remind You of Anything? territory; and Kotetsu's comments about buying a matching pair of fancy pins "just for us" and making it a memory of them spending time together...
Episode 24 has the Ho Yay scene to end all Ho Yay scenes: After Kotetsu (apparently) pulls a Heroic Sacrifice, Barnaby cradles him in his arms and the two start talking—cue dialogue where Kotetsu admits how happy he was when Barnaby first called him by his name, and Barnaby confesses that he's been learning how to make fried rice (which he assumes to be Kotetsu's favourite food), so he can't die right now, goddammit! And the last thing Kotetsu does? Comment on Barnaby's long eyelashes...
According to Matsui, if Kotetsu had actually died, Barnaby would never have recovered from the trauma.
Many Word of God comments (Barnaby prioritizes Kotetsu's safety above everything else; Kotetsu was more or less teetering on the verge of depression before Barnaby showed up; Barnaby's relationship with Kotetsu is the first emotional connection he's made with a human being in two decades; Nishida put way more thought into the Barnaby-Kotetsu rescue scenes than he probably ought to have; etc.) are liable to make one wonder when the two of them will just get married already.
Regarding the bridal carry scenarios:
(From the Roman Album):(About the first "princess rescue") If they had been a man and a woman, they would have fallen in love right then. But with "Ojisan" and "Handsome"...(laughs) (From Monthly Hero 6): The first princess carry was the start of their love [Note: The exact phrase was 馴れ初め (The first meeting of the people who later end up in a romantic relationship. The occasion of falling in love. Start of a romance. Beginning of love.)].
It's indicated that Karina considers Barnaby her rival, and her thoughts are described like this: "Because he is Kotetsuís precious partner, there's a lot about their closeness that worries her".
Comments from the staff:
Matsui(Producer): (About the two after the events of Episode 25) "Barnaby is slightly tsun (itís his nature), but they understand and trust each other so thoroughly that sometimes words arenít even needed."
Masafumi Nishida(Writer): "After [Barnaby] opened up to Kotetsu (as we see at the start of the second cour), he was very happy; and being the "love is blind" type, he was prone to overlooking Kotetsu's faults."
(Regarding Kotetsu and Barnaby after the final timeskip, addressing what he'd like to show in the sequel, should there be one) "Their struggle to lead their lives together might be one of the things we'd like to portray."
Fukuda Nobuaki: "After his parents got killed, Barnaby became twisted and closed his heart—but here comes the amazing Tiger, embracing Barnaby with his great love! When it comes to the human relationships, in the end, it simply really is just ďloveĒ, isnít it?"
Okamoto Nobuhiko: "They build up so many things between them, I think theyíll stay together for the rest of their lives."
(From an interview with Katsuhisa Houki and Hiroshi Iwasaki): "Barnaby is an eccentric, but considering his history and what he shoulders it's probably inevitable. But Kotetsu truly is deeply attached to everything about him, his weirdness and issues included. [...] Both of them long to be told that they are indispensable for the other.
Hirata Hiroaki: But you know, I think that for Kotetsu every face of Barnabyís personality is good—be it his tsun or his dere."
Kaida Yuuko: "When Maverick started getting involved with those two, I couldn't help but snicker. I mean, just look at that dangerous love triangle."
Hidaka Rina: "That's right! It really seemed like another guy inserting himself between the two lovers. Just what do you call this sort of relationship?"
Keiji Andou: "One of the jokingly proposed names for Kotetsu and Barnaby's combined bike form was the "Couple Chaser".
Ozaki has stated that Kotetsu and Barnaby's relationship is left open to the viewers' interpretations, and that the ambiguity has been intentional since the very beginning. Basically; if you think of it as being romantic, that's correct. If, on the other hand, you think of it as Bromance, that's also correct.
From an interview with producers Matsui and Tamura:
Matsui: "If we consider the perspective of the main target audience, which is adult men in their thirties, then wouldn't they be happy to have a young male colleague yearning for them?"
Tamura: "They would?"
Matsui: "And why wouldn't they? Don't you get this impression that a man beloved by somebody of the same sex must be much cooler than a man beloved by somebody of the opposite sex?"
In Special Edition: Side Tiger epilogue, Tamura really wanted to show that Kotetsuís favorite actress looks like Barnaby.
"The two of them are apart precisely because they love each other." (互いに思い合う仲) —Anchorwoman on national television, during the series' feature in Fuji TV morning program. Note: the primary use of the phrase, "longing for each other", "being in love", is to describe relationships in a non-platonic meaning.
Excerpts from the official guides and fan books:
(From the Illustration Book):(Regarding Barnaby in the second half) He didnít go dere or anything, it was love.
(From the pamphlet of HERO AWARDS 2011):(About Kotetsu's expression at the end of Episode 24) "Perhaps due to the feelings of relief and safety brought by his partner's embrace, his expression was serene."
(From Hero TV Fan Book 2):(About Barnaby's views on their decision to quit in Episode 25) "Kotetsu and him are one in soul and body. He was certain they will come back one day." (About Barnaby) "Usually brimming with easy confidence, Barnaby never reveals his weaknesses to other people. But because of how unparalleled he is, even subtle things can wound him—which resulted in the brittle aspect that is prevalent in his nature. The only people who ever managed to see through this and with whom he interacts without pretense are his trusted family and his precious partner" [Note: The "partner" word used here is wholly civilian, not "aibou" or "paatonaa". The exact phrase was 大切な相手].
(From T&B novelization, Barnaby's narration): "And before I knew it, my thoughts, one after another, were drifting to that man"
The first ending theme has a somewhat Ho Yay flavour too. It includes romantic lyrics ("And even if I get analyzed, classified, and deciphered, only I will know who I loved"); Kotetsu and Barnaby running to catch the Memento MacGuffin from Episode 19 and, upon reaching it, clasping each other's hands around it; riding their combined motorcycle outside the city at night and watching the stars together.
Similarly to its ending theme, "Linear Blue wo Kikinagara'' by Unison Square Garden, notably:
Our hearts knit together, with no intention or aim
And the feelings have stirred, unstoppable.
Would you say it's wrong?
Well, I don't give a damn.
It's not for them to decide.
Opening theme for The Rising (sequel movie) "Nemesis" by NOVELS is a passionate love song. There are some weak spots, but overall it's aggressive and assertive. It is meant to represent Barnaby's POV according to the creators.
I will chase after you, until the day I die. (...)
Sing to me, it doesn't matter if we're apart (...)
I'm off to become the pattern of stars / Carrying so many desires along / To bring love or to laugh with you (...)
Yet if there's love still, we will see each other again. / Clumsy or not, I must tell you those precious words here and now / Under the starry sky that connects people together.(...)
How long have I begged so I could be with you? (...)
This picture is apparently official art by Ueda Hiroshi, Tiger & Bunny's manga series illustrator. You can, um... draw your own conclusions about who he ships.
And here's◊ Ueda again. This has to be deliberate.
Nathan (to Karina, about Barnaby): You know what they say, "You always hurt the one you..."
In the opening sequence of a PSP game On Air Jack!, Tiger and Barnaby rise and clasp their hands together, their definitely-not-a-high-five◊ is the main focus for a good few seconds.
A piece of merchandise: an alarm clock, contains recordings of Kotetsu and Barnaby's dialogue which very much evokes an impression of a drowsy pillow talk (they tell each other to wake up or ask for "five more minutes"). Now connect this to the recent declaration that "Pretty much all official works and merch are made to make sense and connect to something else; nothing is made just because"...
And now we finally have our first clue as to how the English dub will deal with the rampant sexual tension. Blue Rose, as of Episode 7, everybody:
Blue Rose: "You two have another lovers' quarrel?"
The Rising provides yet more of this, unsurprisingly. There's the fact that it seems like Everyone Can See It in Sternbild, from Mark Schneider knowing the only way he'd get Barnaby to sign the contract to be moved back to the First League was if he tricked him into thinking Kotetsu would be promoted also, to Golden Ryanof all people seeming to cotton on to Barnaby's attachment to Kotetsu almost immediately and proceeding to not hold back in commenting on it, culminating in him leaving Sternbild partly in order to give Kotetsu his spot as Barnaby's partner back, going so far as to say "they're the only partners for each other", to Karina and Kaede apparently agreeing the best way to help Kotetsu in his apparent depression is to repair his partnership with Barnaby in a very I Want My Beloved to Be Happy way...
Kotetsu nags Barnaby for picking pickles out of his food. Later, when Kotetsu's been fired, Barnaby gets sort of sentimental over a later meal's discarded pickles.
During his enraged lash at Lunatic Kotetsu leaps over a gap between two skyscrapers and smashes his fist into a wall creating a dent in it, fist which was clearly aimed at Lunatic's face. All because he took Lunatic's comment about Barnaby receiving respite from Maverick's death as an insult to Barnaby and his daily struggle to lead a normal life after the events of his youth. He then proclaims he will not let Lunatic interfere with Barnaby's fight and that he has no idea about Barnaby's feelings.
There's also a good bit of this between Nathan and Antonio (Rock Bison) at times; Nathan's lack of respect for personal space is especially apparent in regards to Antonio, and the big man himself always seems to be made a bit too uncomfortable by the attention—almost as if one were putting on airs.
There's no trace of Les Yay in the show itself, but the fifth drama CD hints at Pao-Lin's crush on Karina.
Pao-Lin: "I don't know why, but my heart was pounding like never before."
Agnes: "That look on your face... that's "amour"."
Pao-Lin: "Ms. Agnes, you were there!?"
Agnes: "You guys looked so close, I didn't want to spoil the scene by calling out."
Pao-Lin: "Um, just now...you said "amour"..."
Agnes: "Don't worry so much. You were looking at Blue Rose so intently. Even if she isn't a boy, you can still fall for her, you know."