Table 1 shows that adding estimates from the literature suggests that economists have already explained 177% of the rise in average BMI.

That is from this new NBER paper, by Courtemanche, Pinkston, Ruhm, and Wehby, which seems to be one of the most careful studies to date. They do it right and then offer some more commonsensical conclusions:

A growing literature examines the effects of economic variables on obesity, typically focusing on only one or a few factors at a time. We build a more comprehensive economic model of body weight, combining the 1990-2010 Behavioral Risk Factor Surveillance System with 27 state-level variables related to general economic conditions, labor supply, and the monetary or time costs of calorie intake, physical activity, and cigarette smoking. Controlling for demographic characteristics and state and year fixed effects, changes in these economic variables collectively explain 37% of the rise in BMI, 43% of the rise in obesity, and 59% of the rise in class II/III obesity. Quantile regressions also point to large effects among the heaviest individuals, with half the rise in the 90th percentile of BMI explained by economic factors. Variables related to calorie intake – particularly restaurant and supercenter/warehouse club densities – are the primary drivers of the results.

Here is a much earlier ungated version of the paper, with differing numerical estimates, use with caution. A few related studies you will find here.