Obesity is self inflicted. As such you should be made to pay for your own health care. Same with smoking, drug and drink related hospital treatments.
And sports injuries, RSI, hernias, ...?
Don't trivialise the subject. Smoking, drinking and eating are all addictive. Smokers can just quit, with help. Alcoholics can go t-total, with help. Eaters cant just go (wait for it

Many overweight people aren't overeating just to be fat and lazy. Theres deep routed issues at the heart of it. Most have very low self-esteem, for a reason, and that is only exasperated as they gain weight through comfort eating. Exercise is harder, not only physically, but mentally too as their low-self esteem kicks in when they try to exercise, they cant do much, which is demoralising, and the worry of people seeing them makes things worse. Because lets be honest. We would all laugh to ourselves if we saw a fat lass jogging.
No amount of dieting and exercise is going to work until the root of the problem is worked on for each individual. Their weight will just yoyo their whole lives and they wont ever be healthy.