He could also become withdrawn and depressed.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.
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.
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.
She becomes very focused and single - minded. In a fanfic where Percy is poisoned, Annabeth quickly starts to research all possible antidotes. She interrogates other characters who might know something, and she doesn't rest until she has a lead. She also gets very emotional in private. She might cry when she thinks no one is looking because she's so afraid of losing Percy. But in front of others, she's strong and in control, leading the search for a solution to save him.
She might be heartbroken at first. She could try to jog Percy's memory by showing him things that were important to them.
Well, in many such fanfictions, Percy might be extremely flustered. He could blush furiously and quickly look away, being the gentleman that he is. After all, he has deep respect for Annabeth.
He could also become angry. Percy has a bit of a temper, and he might lash out at Annabeth, demanding an explanation. He might feel betrayed, especially if he doesn't understand the real reasons behind the break - up. In his anger, he could distance himself from their mutual friends and go on solo quests to clear his head.
Well, Percy is a complex character. His reaction could depend on how much he knew about the pregnancy before Annabeth left. If it was a complete surprise, he might be in denial for a while. He could also start to blame himself, thinking he had somehow failed her. And then he might eventually turn that pain into a determination to be a better person, whether or not he ever sees Annabeth again.
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.
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.