Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: Gravity Falls
"Mabel's not here. She's in sweater town."
In a sort of screwed up way: "It's better this way for Paper Jam Dipper."
It's kind of hard not to feel bad for Tyrone when he dies.
Dipper: Tyrone! You were the only one who understood.
In Dipper vs Manliness, while Dipper pulled a Cry Cute, it's so hard not to feel sad for him.
In "The Time Traveler's Pig", Dipper and Mabel meet a time traveler, and Dipper uses the time traveler's device to go back in time to ensure that he doesn't hit Wendy in the face with a baseball, and so that Robbie wouldn't ask her out. However, this requires Mabel's help, and because of this, Mabel misses out on winning a pig, who became her best friend. She's so distraught about it that she ends up losing her mind and left banging he head against a totem pole for at least a month (most likely far longer, if not permanently) until Dipper decides to set things right and lose out on a chance with Wendy.
As Dipper rambles about trying and failing to change the past...
Wendy: You lost me, dude.
Dipper: I know.
His whole reaction the first time Robbie asks her out is just soul-crushing.
Mabel giving Dipper the cold shoulder in Summerween, because she thought Dipper didn't care about her as much as he did for Wendy.
While Mabel feeling betrayed is bad enough, imagine how regretful Dipper was.
Also, Mabel's explanation why Dipper going trick-or-treating was so important to her: the twins are getting older and she's afraid there won't be many Halloweens left together.
And she seals off this by stating that she didn't realize until now that this one was going to be her last one. As if she's finally accepted that her brother is never going to trick or treat with her ever again. Wow..
Mabel: That's exactly why we need to, Dipper! We're getting older, there aren't that many Halloween's left...(sigh) I guess I didn't realize this was our last one...
It gets worse if you take it that she had accepted the fact that they were all probably going to die.
Dipper taking everyone's teasing about his voice cracking to heart in "Bottomless Pit" and drinking the tonic that changes his voice only to freak everyone out and still not be accepted. By the end of the story, he's crying, being chased, and basically miserable. It's impossible to not wanna hug him when he goes back to the junkyard.
Dipper: I even sound ridiculous when I cry!
Stan's downer speech about life in "Bottomless Pit." Sure, it's hilarious in how abruptly out of nowhere it comes, but the thought that Stan secretly ponders such bleak things is pretty depressing.
That poor, poor kid stuck in solitary confinement in "The Deep End." He was completely forgotten about. For an entire year.
Mermando missing his family. It's hard not to feel for him when he makes that sad little dolphin squeak.
Mabel and Mermando's goodbye.
Mabel's little speech to Dipper towards the end can get to some people.
"Dipper! Don't you know what it's like to fall for someone... even though you know in your heart it'll probably never work out... but you would do anything for that person?"
Dipper and Mabel's confession that they never wanted to move out of their rooms. It leads to Dipper telling Mabel how he feels when she brings Candy and Grenda over so he has nobody to hang out with. It pretty much makes Dipper realize that Mabel is the closest thing he has to a friend his own age anywhere in Gravity Falls, and probably everywhere he's been.
Its very easy to miss, but the shocked look on Mabel's face when Dipper suggest they sleep in separate rooms. You can tell Mabel was hurt by the mere thought of Dipper not wanting to share a room with her.
Wendy's break-up with Robbie in "Boyz Crazy", and her response to Dipper after he asks her to hang out. Dipper treats it as his victorious moment without giving Wendy breathing space to deal with what is a tragic moment to her. Even if you rooted for Dipper from the beginning, you can't help but feel a little bad...
No love for Mabel? She's keeping Sev'ral Timez in her room even though Candy and Grenda are asking her to let them go. Mabel's response is that every boy she's fallen in love with has left her (Norman turning out to be gnomes, Gideon trying to kill Dipper, Mermando leaving to find his parents). And in the end she gets a massive guilt trip from a song which is enough to let the band go free.
That song Sev'ral Timez sang to Mabel, who basically kidnapped them and forced them into hiding and doing what she wanted. It was sad because A) the guys can't bear to show malice to the girl who actually rescued them, so they guilt-trip her, and B) they acknowledge that Mabel DOES care about them, while also expressing their need to be free.
Sev'ral Timez:(singing) Mabel girl, we know you love us so!
You can't help just wanting to give Dipper a hug when he thinks that Stan wants to get rid of him.
In "Gideon Rises" - when Dipper and Mabel have to leave town, leaving Stan, Wendy, Candy, and Grenda behind. The latter two are holding each other sadly.
The fact that Wendy looks forlorn as the bus drives away really says something.
You can tell that things are at their Darkest Hour when they don't even make a joke at the act break.
Earlier, when Stan lies to Dipper and Mabel's parents about the living conditions. You can see him slowly come to the conclusion, both during and after the phone call, that the situation is too much for the kids anymore.
Poor Waddles cowering in fear of Gideon when he shouts at him to get back in his corner.
Notice how Mabel's legs are tucked into her sweater on the bus ride. She's in Sweater Town.
Dipper and Mabel desperately trying to hold on to each other as the Gideon-bot picks them up.
Gideon's taunting of Dipper in this episode was just awful, especially if you've ever though little of yourself. Gideon is just rubbing it in Dipper's face that he's a weak little kid, which is Dipper's worst fear.
Gideon: What are you gonna do? No muscles, no brains...face it, kid! You're nothing without this.
Stan receiving all three books, as it's revealed that Stan really DOES know more than he lets on, and that he just unlocked a secret that might change Gravity Falls as we know it is sure to shed some Manly Tears.