Science on obesity is fairly incomplete still as well. It is more of reenforced ideas about obesity being pushed and using science to try to validate it without having the data collected to back it up. I am not sure about the immune systems, but 'heathly' people are far more likely to need to be rescued from a mountain, be in biking accidents, bitten by a poisonous snake, shit I am betting even STDs are more prevalent. In a lot of ways being fat just seems like a nice social protection. Kind of like societal body armor.
But we do have government programs aimed at reducing obesity. If the government really wanted to curb it, they could do more by just unsubidizing sugar and meat. Put huge taxation on fast-food, high caloric foods, and remove candy from every single non-food based business.
I think the authority is a 'you don't have the right to harm other people because you want to be ignorant' kind of thing. Being fat is not a danger to anyone but yourself. Spreading measles because Jesus told you your ancestors road dinosaurs and science is bad is a danger, so I don't vaccinate my kids, to anyone they come in contact with.