Another possibility is that Percy would use it as motivation. He'd prove Annabeth wrong by using his street - smart skills and quick thinking. For example, in a battle or a quest situation, he'd come up with a clever solution that shows his intelligence in a different way than Annabeth might expect.
Then, she would probably be angry. Annabeth is a strong - willed character. She would feel betrayed and used, and her anger would fuel her to find out the truth. She might start her own investigation to figure out what's really going on with Percy, whether he's been influenced by someone or if there's another reason for his actions.
He could also become withdrawn and depressed. Percy and Annabeth have a very strong bond, and her death would leave a huge void in his life. He might isolate himself from his friends and family, lost in his grief and memories of her.
Well, Percy could have a range of reactions. At first, he might be in denial, not believing that Annabeth would actually leave him for a job. Then, as it sinks in, he could get angry. He's a passionate guy, and this would be a big blow to him. He might also feel a bit of envy towards the job that seems to have taken Annabeth away from him. In the long run, though, he could use this as a chance to grow on his own and become more independent.
Percy would be completely devastated. He might go into a state of shock at first, unable to believe that Annabeth is really gone. Then he could become filled with rage, vowing to take revenge on whoever or whatever was responsible for her death.
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.
At first, Percy could be in denial. He might think that there's some misunderstanding, that Annabeth doesn't really mean to break his heart. So he tries to talk to her, to make things right. But as the truth sinks in, he could be really depressed. He might lose his appetite, not be able to sleep well, and just generally seem like a shell of his former self. His whole world revolved around Annabeth, and now that it's falling apart, he doesn't know how to cope.
He could become withdrawn. Percy might start to distance himself from Annabeth, not wanting to be around her if she's going to be cruel. He might go off on his own and think about what she said, trying to figure out if he did something wrong.
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.