Maybe it’s because I’m able to separate the two, but I have no problem with OUAT’s version of Belle.
In Belle’s defense, (because I just watched the episode a few hours ago), this episode was supposed to show the early days of rumbelle. She was taken away from her family and friends with the possibility of never seeing them again. Who wouldn’t cry in a situation like that? If she didn’t show any kind of negative emotion about being separated from her family, that would not be healthy at all. So it’s okay for the girl to cry about that.
But it doesn’t make her weak.
I agree about the context thing. In addition, I think she can not only see the best, but probably it’s opposite too — the worst in people.