Why shouldn't there be a "Fat Tax" for the overweight?

Why shouldn’t there be a ”fat tax” for those who are obese? A study released by the National Bureau of Economic Research determined that medical treatment involving obese people cost 168 billion, that is billion with a “B”, and I am sure they are not footing the bill for all of it. Should the rest of us who bother to take better care of ourselves be penalized for it in higher premiums? It isn’t like obesity isn’t avoidable in most people, it don’t strike out of nowhere like liver cancer or Parkinson, most people created the situation themselves. Larger beds, wheelchairs, MRI machines cost more, a cost passed on to all of us when it benefits way less. Maybe a “fat tax” will motivate them to do better.