The statistics here are saying anywhere from 30-50% of each American state's population is obese so yeah I'm gonna venture to say food deserts are not the culprit here

Edit: Looks like the AECF link might've been edited as the Google preview said 8% - indeed is 12% on the same link. USDA says 10%: https://www.usda.gov/media/blog/2011/05/03/interactive-web-t...