Annabeth would be in a tough situation. On one hand, she has to take care of herself and the baby. On the other hand, she's desperate to find Percy. She may be feeling a mix of fear, anger, and determination. She could be using her intelligence to analyze any clues that might lead to Percy's whereabouts. She might also be reaching out to any allies she has in the mythological world, asking for their help in finding Percy.
Well, Annabeth is a strong character. She may start by grieving privately, not wanting to let her vulnerability show. As she is pregnant, she would feel an even greater sense of responsibility. She could start documenting stories about Percy for the baby, so that the child can know who their father was. And she would probably try to find a new purpose in life, centered around raising the baby in a way that Percy would have wanted.
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.
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.
One reason could be that he was framed for a crime he didn't commit and had to run away to clear his name. In the complex world of the fanfiction, there could be a conspiracy against him. Some powerful beings might not want him to be with Annabeth or have a child, so they set him up and made him disappear.
Annabeth becomes more worried and determined to find him. She might also show a more vulnerable side as she deals with his absence.
She might focus on her studies more. Since Annabeth is really into knowledge, she could pour all her energy into her schoolwork, like spending extra hours in the library or on research projects.
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.
Their relationship might develop through more in - depth conversations. Since they are engaged, they start talking about their future, like where they want to live. Maybe Percy wants to live near the ocean and Annabeth has other ideas, and they have to compromise.
She might be heartbroken at first. She could try to jog Percy's memory by showing him things that were important to them.