Perhaps she's being bullied. In the wizarding world, there could be other students who pick on her because she's a 'Mudblood'. This could be really distressing for Hermione, and when Snape finds her crying, he might be conflicted between his general dislike for Gryffindors and his sense of justice.
Another possibility is that she had an argument with a friend. It might not even be Ron. It could be with Harry or another Gryffindor. She's very sensitive about her friendships and any conflict could make her cry.
Well, it could be that he's feeling the weight of his destiny. Harry has so much on his shoulders, like fighting Voldemort. Maybe he just had a particularly tough encounter with the Dark Arts or lost someone dear in the fight against the dark side. Another reason might be his feeling of isolation. Despite having friends, there are times when he feels alone in his battle.
It could be that she's homesick. Even though she loves being at Hogwarts, sometimes she might miss her muggle family a great deal. Also, she might be crying because she's being bullied. There could be some students who are jealous of her intelligence and are giving her a hard time. In the fanfiction, Sirius finding her crying might lead to him becoming a sort of mentor or protector for her, helping her deal with whatever is making her sad.
Perhaps he's had a falling - out with his friends. In the Slytherin house, there could be a lot of power dynamics and rivalries. If he's been betrayed by someone he thought was a friend, it would be very upsetting.
Isolation. Snape is a lonely character. He doesn't have many friends, and he is constantly in a difficult position between the Death Eaters and the Order of the Phoenix. His feeling of being alone and not being fully understood by anyone can lead to crying in fanfiction.
Perhaps he's feeling guilty about something that happened during one of his quests. Maybe he made a decision that had negative consequences for someone he cares about, and that's weighing on him. It could also be that he's just had a really tough encounter with a powerful enemy and is letting out the pent - up stress and fear through crying.
One possible reason could be that she's had an argument with a friend at Hogwarts. Maybe she felt betrayed or misunderstood by someone she trusted. For example, if there were rumors spread about her, it could really hurt her feelings.
One possible reason could be remorse. Harry might realize that he misjudged Snape all along. Snape had a complex role, and if Harry discovers the truth about Snape's true loyalties and sacrifices, it could lead to him crying out of guilt for how he treated Snape in the past.
Perhaps Hermione is facing some sort of interpersonal issue. She could have had an argument with her friends, like Ron and Harry. In the wizarding world, friendships are crucial. If there's a rift in their relationship, it would deeply affect Hermione. McGonagall, being a perceptive teacher, might then try to mediate and give Hermione advice on how to handle the situation.
One possible reason could be unrequited love. In the fanfic, Chansung might be in love with someone who doesn't feel the same way. This could lead to a deep sense of sadness and cause him to cry. For example, he might have confessed his feelings but been rejected, leaving him heartbroken.