But neither private insurance nor hospitals have any incentive to operate preventatively because insurance can just increase premiums and everybody happily makes more money... Some might observe how that also increases the GDP...
The USA doesn't do much of that though. It prefers medical care.
(E.g., adding a dose-dependent sin tax on food-like substances with added sugar, subsidizing real food for those on SNAP. Unpopular because who doesn't want their simple carbs?)
America does a lot of that, often quite well. It just isn’t provisioned equally, geographically or class-wise.
The only other thing I can think of that would affect state wide obesity is food security and quality. Proper healthcare would be my first pick for fixing obesity.
For instance, if you cut preventive healthcare for younger parts of the population that will take longer to manifest.
I wish there were more modeling tools available to run what-if simulations on public data.
That being said, a relatively large proportion of US GDP is driven by healthcare, which is normally measured at cost in the UK and Europe.