While both Rocky and Apollo are in the hospital at the beginning, Rocky visits Apollo and asks him a single question: "Did you give me your best?". Apollo's response was yes. This proved to Rocky that he is a great fighter and that it wasn't a fluke that he fought Apollo for 15 rounds.
Rocky: Thank you.
Even more than that, despite any anger or irritation Apollo might have had with Rocky, he didn't lie or tell him to go away. He was sportsman and man enough to tell Rocky the truth. For all of his showboating and arrogance, Apollo will still give credit where it's due.
After getting out of the hospital, Rocky takes Adrian to the zoo and proposes to her in his own casual, Adorkable way. She says yes.
One of the main reasons Apollo wants a rematch with Rocky, other than people calling "foul", is that they are insulting his kids at school. He might be obsessive at this point, but he's still the same man who loves his family and won't take any insults towards them.
Paulie, who was previously using Rocky for his own desires, now is a really good friend of his, who is willing to give him a handout whenever Rocky needed it. He even goes as far as to berate his sister for being un-supportive of Rocky.
It's also noticeable that his relationship with Adrian has improved greatly. He's become a genuinely better person.
After Rocky and Adrian get married, he carries her all the way home in his arms.
Rocky: You know, I never knew you were so light, you know?
Adrian: No?
Rocky: No. If I did, I would've carried you everywhere.
Their wedding night is also a pretty tender scene:
Adrian: I hope nothing changes...
Rocky: I ain't changing and I sure ain't never changing nothing about you.
Adrian: I love you.
Rocky: I love you too.
The way Mickey can show protectiveness and concern for Rocky. When Rocky considered fighting again and tried to convince Mickey to train him, he slaps him on the right side of the face and got him to face the truth about his bad eye.
"...you didn't see that coming, did you? And that was from an old broken down bum like me. What do you think that champ will do to ya?"
Mickey does give Rocky a job at his gym, but he has too much respect for Rocky to let him be seen carrying out mundane tasks, and worries that the guys will not respect him as much. He finally gets fed up with the humiliation that Rocky is going through, part of it thanks to Apollo Creed, to the point where he goes full on Papa Wolf and decides to train Rocky again.
"I say we knock his block off, kid!"
Despite being disgruntled towards Rocky's poor performance in training, he decided to stay with him while he's going through his Heroic BSoD, even if it means failing the fight.
"Well if you're gonna blow it, I'll blow it with you."
Despite going through hard times, it's heartwarming to know that Rocky is doing everything he can to NOT do anything illegal anymore, just for Adrian's sake.
During the climactic fight with Apollo Creed, both Adrian and Paulie are at home, so apart from Mick and his corner crew, Rocky has no one he personally knows at the ring to support him. Except for one. Numerous times during the fight, we cut to none other than Tony Gazzo, Rocky’s Loan Shark former boss. When Rock takes the title, Gazzo ROARS his approval.
Rocky and Mickey hugging in the ending, after all the hardship Rocky went through. Manly Tears were shedded.
Also, after he wins, the first person he credits is Mickey for training him. Mickey hangs his head in gratitude, because at long last, the name of Mickey Goldmill will be acknowledged in the annals of boxing history.
Despite being antagonistic towards Rocky the whole movie, Apollo acts like a Graceful Loser when the former wins, raising Rocky's hand and patting him on the head to congratulate him, and Rocky in turn thanks Apollo for fighting him.
While Rocky is delivering his victorious speech, a man on the audience shouts "We love you, Rock!", to which he responds "I love you's, too!".
And of course, the film's most famous line, from Rocky to his wife at home:
"Yo, Adrian, I did it!"
A retroactive example: Rocky III confirms that Mickey is Jewish, and yet he visits Christian/Catholic settings, out of respect for Rocky.
After Rocky went through his running alone in the first film, this time he's a hero to the neighborhood and is joined by seemingly every kid in Philadelphia.
