If the western world's obesity rates were lower, how much less money a year would these countries spend on food?

They would probably save a lot more on medical expenses than on food since a lot of obesity results from the consumption of cheap food whereas the medical expense for dealing for diabetes and related illnesses is enormous.   The money could be spent for nutrional education and for other social programs that would contribute the quality of life of all citizens ... if the political process were geared towards motivating legislators to satisfy citizens rather than campaign contributors.

They might actually spend more money to get to less than 5% obesity. Good, wholesome, organic, fresh food isn't usually cheap. Grass fed beef and free range chickens, eggs from free range chickens cost more. There are OBVIOUS connections between obesity and a salty fatty delicious big mac and tasty fries with a super sized soft drink.   The diet that makes people fat is less expensive and more widely available. See your nearest fast food joint. versus Guess which probably cost more?

Probably quite a bit, and if obesity went down so would health care expenditures.

Classic case of wrongful Public Policy. Politicians are only motivated to plan for only a couple of mandates into the future (never liable for what happens decades after). This often results in solutions optimized solely for the short-term - at the expense of sustainable, sensible long-term policies. Policies that do not combat (and indeed encourage) high on fat, salt and sugar foodstuffs, are popular until the onset of lifestyle diseases much later on (decades after the fact). In the mean time, the apparent abundance of  accessible (cheaper) and tasty foodstuffs pleases the populace (false wealth feeling). Deregulation (for producers and middlemen) also give a (temporary) boost to the produce and food processing economic sectors. Even not considering how competitive your exports become. Hence the special interest pressure groups. Public health policies configured to control obesity and incentive correct eating and exercise habits, only became obviously important to a society when it becomes easily demonstrable the personal and societal costs (aggregate health care costs, worker overall productivity, etc.) of not going down that path - now - with the current generation.