in the text that Fanny uses tears as a weapon for sympathy, consciously or not. She is simply not that kind of person. Fanny is a sensitive soul, who has endured a lot of pain and suffering. Why should she not cry? It would be strange if she didn't.

I think many people have the unfortunately wrong idea that tears indicate cowardice or immaturity. It's not like Fanny sits around moping and crying in front of people and avoiding work. Except for the day of her arrival, her tears are shed in private. Edmund accidentally stumbles upon her crying once.