The problem is that obesity is a matter of social class. People who depend on food stamps and the like are generally subjected to eating food containing high quantities of sodium, which causes obesity and heart problems. It is not merely a matter of exercise. Exercise is good, of course, but what really matters is what you eat, and what you eat is determined by your access to quality food, which is determined by your parent's income.
It has been demonstrated in studies, if i remember correctly, that exercise is good for maintaining healthy body weight but not necessarily losing a significant amount of weight. By blaming children who are not receiving appropriate food for their inactivity, yes you are bullying them by creating a new layer of stigma against them without really addressing the issue.
If we really want to eliminate obesity, we need to put sodium restrictions on food and alter government subsidization of foods. Most subsides go to corn and meat, and almost none go to vegetables/legumes. That is the real problem.