Japan and Colorado have just as much access to cheap calories as Louisiana, but notably less obesity. Also, obesity rates have increased faster than access to calories has; it's a surprisingly recent problem.
Even in the eighties, household spending on food was nearly 50% higher relative to overall consumption than today.[0] Japanese households today actually spend 16%(!) of their household income on food, compared to only 7% in the US.[1]
Obviously there are multiple factors, as I said I think the relative satiety of food also plays a role. US food spending has been more or less static over the last two decades while obesity rates have continued to climb so cost can't explain everything (though as an aside, I do think lower costs probably take some time to have an effect). But even if there are multiple factors at play, cost really should not be discounted as a huge driver, especially if we're taking a public health approach to addressing the problem. If we just attribute obesity to individual moral failings, as some are wont to do, I think we're really doing a disservice to ourselves
