Another possibility is that she tries to find allies. Since Annabeth is smart, she'd understand the power of having others on her side. So she could start by confiding in some of her closer friends in the HS setting of the fanfic, like maybe Grover if he's around. They could then work together to figure out a solution to Percy's bullying behavior.
She might initially be shocked. Annabeth is a strong character, so she could start by trying to stand up to Percy verbally, asking him why he's being so mean.
He could become withdrawn. Percy is a sensitive person at heart. So if Annabeth's actions are really hurtful, like if she cheats on him in a fanfic (although it's a very sad scenario), he would likely isolate himself from her and their friends. He might go off on his own to think things through and deal with his pain privately.
Annabeth might be initially in awe of Percy's new godly status. But she would quickly start thinking about how to use this new situation to their advantage. She is practical, so she would likely start planning how they can better protect their friends and the world.
Percy could stand up to Annabeth. He's a strong character. He might confront her directly about her bullying behavior and tell her it's not okay. This could lead to a turning point in their relationship, where Annabeth realizes she's been wrong.
She might be initially very angry. Annabeth is intelligent and perceptive, so she would likely feel betrayed that Percy thought he could deceive her. For example, if Percy lies about a mission, she could find out the truth later and confront him immediately, demanding an explanation.
Annabeth could also be angry, not at Percy but at the situation or the forces that led to his death. She might vow revenge and start on a journey to find out who or what was responsible for Percy's sacrifice and make them pay. This could lead her into a whole new set of adventures and challenges as she tries to come to terms with her loss.
She might be heartbroken at first. She could try to jog Percy's memory by showing him things that were important to them.
On the other hand, she could try to honor Percy's sacrifice. Annabeth might focus on the reasons why Percy died for her and strive to fulfill any tasks or goals that he might have hoped she would achieve. She would carry on his legacy in a positive way, even though she is heartbroken.
Annabeth could also try to solve the problem that's making Percy cry. If it's related to a quest or a danger, she'll start thinking of ways to fix it. In some fanfictions, she might say 'Don't worry, we'll figure this out together.' and then start making a plan.
Well, a major theme is relationship development. Whether it's their friendship or the budding romantic relationship between Percy and Annabeth. It shows how they interact with each other, understand each other better, and grow closer over time. Also, the theme of facing challenges together is quite common. They encounter various problems in high school, both ordinary and extraordinary, and they rely on each other to get through them.
One great 'Annabeth Percy HS stories fanfic' is 'High School in the Gods' Realm'. It has an interesting plot where they face modern high school problems along with mythological challenges. The character development is well - done, making it a must - read.