I mean, if we were confident one particular food source contributes more to obesity than others, we have a solution that we know would work: tax it (and ideally dedicate revenues to some kind of universal food tax credit). People would consume less of it at the margin and then be less obese.
It would rankle some people, but so do taxes on alcohol and nicotine. My big concern is that I'm skeptical whether we can really identify those "bad" foods and that even if we could whether we could ensure the government would whitelist/blacklist the correct foods.
As far as lack of control goes, I'd be curious if fatter/poorer people would do worse on some kind of adult marshmallow test. Maybe see if you can get them to sit perfectly still for 20 minutes in exchange for a monetary reward. I don't have a strong sense that they'd do worse than skinnier/richer people.
