If you tell someone they’re fat when they are, in fact, underweight, they hopefully won’t believe you, but if they do believe you, provided they live long enough (anorexia can kill), odds are good there will come a day when they stop believing you.
After that if you tell that person they’re fat when they are, in fact, a healthy weight, you’ll probably hurt their feelings, but odds are good they won’t really believe you. (And if they do, you’ve just pushed someone back into anorexia, so stop it!)
But if after all that, that same person starts becoming dangerously overweight, you know who they probably won’t believe? They probably won’t believe the people who actually care about them and their health because you (or people like you) have been telling them for years that they’re fat, and they are now so done with the topic of their weight.