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Tear Jerker: The Heroes of Olympus
Percy calls home for the first time in months and gets the answering machine.
The later part of Hazel's childhood, particularly her death.
Heck, Leo's whole childhood. Accidentally burning his mother alive and then being kicked out by his own family.
At the end of The Lost Hero, after talking to her father, Piper thinks something like 45 seconds? Maybe even a full minute. It wasn't much, but it was a start. To repeat: Piper thinks a full minute alone with her father is good. Busy as he was, despite his good intentions, Tristan McLean is a shit parent.
Leo's mother. 'Nuff said.
Ella. Poor, poor Ella.
Thalia talking about what happened after Jason was taken away.
Nico’s eyes looked like shattered glass. Percy wondered sadly if something inside him had broken permanently.
Annabeth's story about the spiders in her bedroom when she was a child. Also Nightmare Fuel.
Following the declaration of war between the Romans and the Greeks, the gods all go a bit wonky due to the schism. While most of them are hit very hard by this, Athena takes the cake. When Annabeth sees her, she resembles a slightly off homeless woman and (at least temporarily) disowns Annabeth because of her daughter's insistence that peace can be made between the Greeks and Romans.
What the Romans did to Athena was also pretty horrible.
Everything about Nico. Not only had the poor kid just gotten out of the Greek Mythological Hell Pit, but now we find out that he's gay (or bi) and has/had a crush on Percy. Percy who fell into Tartarus to stay with his girlfriend. Not only does he have to deal with the pain of knowing the person he loves most is going through the horrible trauma that he did, but Nico was born in the 1930's! Imagine how ashamed he must feel! It also just adds to his feelings of isolation.
The whole scene where this happened was just heartwrenching. Eros/Cupid, God of Love, is just goading Nico on, forcing him to reveal his true feelings about Percy, while all Jason can do is listen. It broke this troper's heart.
Nico:I had a crush on Percy. That's it. That's the big secret. Happy now?
And this scene:
Jason: You know, no one's going to judge you.
Nico: Really? That would be a first. I'm the son of Hades, Jason. I might as well be covered in blood or sewage, the way people treat me. I don't belong anywhere. I'm not even from this century. But even that's not enough to set me apart. I've got to be- to be-
He's so ashamed he can't even say the word.
Now think about this: Hazel, Nico's half-sister, also grew up in the 1930s, dying in 1942. Even if he were to accept Jason's more modern sensibilities toward homosexuality, he'd have every reason to believe his sister wouldn't.
Annabeth wandering around blind, thinking Percy's abandoned her while he's forced to watch. Pretty much the entire Curse scene was this with Nightmare Fuel.
Leo and Calypso. Full-stop.
Annabeth overhearing Bob and Damasen talking about how long it's been since they've seen the sun. The way Damasen especially sounds is sad and hopeless because he's been in Tartarus for so long that he's lost hope to ever see the surface.
Damasen: Yes. It was yellow. When it touched the horizon, it turned the sky beautiful colors.
Bob: I miss the sun. The stars, too. I would like to say hello to the stars again.
As a matter of fact, Damasen's backstory can be considered a Tearjerker too when you realize he's only in Tartarus because he was trying to avenge his farmer friend.
In the final chapter of House of Hades, Percy tries to thank Nico for guiding the others and for indirectly saving his and Annabeth's lives by being nice to Bob and convincing him that Percy was a friend, even though Percy never gave him a second thought. Percy's trying to live up to his resolution in Tartarus to start treating the people around him better— he specifically singles Nico out among those. But Nico is being distant and dismissive towards him, and Percy's inner monologue goes on a bit, noting how much Nico has changed over the years and lamenting the fact that he's never been able to understand Nico and he doesn't know why. By this point, the reader knows it's because Nico had a crush on Percy, and there's evidence that, despite what he says, he's not really over it and has a hard time dealing with Percy being oblivious, being with someone else, and just the fact that he grew up in the '30s/'40s and is ashamed of liking dudes. The tragedy comes from the fact that Percy wants to understand Nico and do right by him, but Nico just can't let that happen.