Of course obesity is a public health problem.
But do you really think that the people who "fat shame," to use the sjw term, do it because they are considering the strains that the obesity epidemic puts on the public health system? I don't. I think that when people make fun of overweight people for being fat, they're doing it because they're assholes and they don't like they way that the victims of their bullying look.
The last time I checked, I was slightly underweight. I eat an awful, fatty, greasy, meat-based diet, and I rarely get any exercise at all. I certainly never do anything with the express goal of getting exercise (If I ride my bike or play a game of basketball, it's because I want to ride my bike or play basketball). Nobody judges me for it. Nobody tells me to change anything.