They might decide to sneak out just to have some alone time away from the chaos of their normal lives. In their world, there's always so much going on with training, quests, and dealing with other demigods, so they could be craving some peace and quiet together.
Maybe they suspect something fishy is going on in their camp or the surrounding area. To avoid causing panic or being stopped by the authorities in the camp, they choose to sneak out to investigate on their own. They trust their own instincts and abilities more than anyone else in this case.
It could be because he wants to give her a special gift without her knowing. So he sneaks in to leave it on her bedside table.
He could be a bit shy. Since he also has feelings for Annabeth but was too nervous to make the first move. So when Annabeth asks him out, he blushes and stammers a bit, like, 'Uh, yeah, Annabeth. That sounds great.' And then he would be really happy inside, thinking about all the things they could do together on their date.
He could be frustrated with her. Maybe they had an argument earlier, and Percy, not knowing how else to express his feelings, throws the apple as a way of getting a reaction from her. It's like a childish way of saying 'I'm mad at you' without using words.
Another reason could be that Percy wants to start a conversation about Annabeth. By showing off the fanfiction, he can get people talking about her character, her strengths, and her role in their world. This could lead to more in - depth discussions about her and also about the whole story universe they are in.
One reason could be to add a new twist to the story. By making Percy smarter, it changes the power dynamic between them and creates new plot possibilities.
Another possibility is that there could be external forces at play. In some fanfic storylines, there might be a prophecy or a powerful enemy that convinces Annabeth that leaving Percy is the only way to protect him. She might sacrifice their relationship for his safety, believing that her presence endangers him in some way.
She might be interested because she cares deeply about Percy. Reading about his experiences in the Styx, even in fanfiction, could be a way for her to understand him better on a different level.
Well, it could be because Sally is an important person in Percy's life. He trusts her and wants to share the interesting things about Annabeth from the fanfiction with her.
He might do it out of pure affection. Percy really cares about Annabeth, and playing with her hair could be an instinctive way to show his love.
It could be their friends like Grover. Grover is always around them and he might accidentally stumble upon them while they are in a private moment.