They might cuddle because they've been through a lot together. All the battles and quests have made them rely on each other. At camp, it's a place of relative safety where they can finally let their guard down and be affectionate.
Perhaps there's a new threat looming over the camp. Percy and Annabeth are worried but also determined to protect it. One night, while on patrol, they stop at a lookout point. The night is cold, and they huddle together for warmth. As they do, they realize how much they mean to each other and start cuddling. It's a moment of vulnerability and love in the face of danger.
It could be that Annabeth has a misunderstanding about Percy. She might think he's a threat to her position or status at the camp, so she bullies him to try and keep him in check.
It could be Chiron, the centaur. He's always keeping an eye on the campers and would likely be concerned if he caught them up to something. He might give them a stern talking - to and some extra chores as punishment.
A really nice moment could be that they are cuddling in bed after a long and tiring adventure. Percy has his arm wrapped protectively around Annabeth. They are both looking at the stars through the window above the bed, and Percy says something like 'I'm so glad you're here with me, safe and sound.' And Annabeth just snuggles closer in response.
Cuddling can be a way for them to show vulnerability. Percy, who is often seen as strong and brave, shows his softer side when he cuddles with Annabeth. This makes Annabeth see him in a new light and deepens her love for him. Each cuddle session is like a step forward in their relationship, as they become more comfortable with being close and sharing their emotions.
Maybe they're in a cold, enchanted forest. They build a small, cozy fire. Percy wraps his arms around Annabeth from behind as they sit in front of the fire. Annabeth leans back into him, and they cuddle to keep warm. They start sharing stories from their childhood, their voices low and soft, creating a really intimate and heartwarming atmosphere.
Perhaps they were caught in a compromising position while having a private moment. This could lead to all sorts of awkwardness among their friends at the camp. They might have to face some teasing or even get in a bit of trouble with the camp counselors for not following the rules.
There probably is. Fanfiction is a vast world full of different interpretations of characters and their relationships. Percy and Annabeth are popular characters, and it's not uncommon for fans to explore their romantic interactions in different settings, including at camp. But make sure to check the ratings and reviews of the fanfictions you find to ensure they meet your expectations.
Percy might stand up for himself. He could use his own skills and strengths, like his control over water if that's part of the fanfiction's universe, to show Annabeth that he's not an easy target.