The full article is gated but the abstract is unequivocal about the findings:
The prevalence of obesity has doubled over the last 25 years. We estimate the effects of multiple socio-environmental factors (e.g., physical demands at work, restaurants, food prices, cigarette smoking, food stamps, and urban sprawl) on obesity using NLSY data. Then we use the Oaxaca–Blinder decomposition technique to approximate the contribution of each socio-environmental factor to the increase during this time. Many socio-environmental factors significantly affect weight, but none are able to explain a large portion of the obesity increase. Decreases in cigarette smoking consistently explains about 2–4 % of the increase in obesity and BMI. Food stamp receipt also consistently affects the measures of weight, but the small decrease in food stamp program participation during the period we examine actually dampened the increases in obesity and BMI. Collectively, the socio-environmental factors we examine never explain more than about 6.5 % of the weight increases.
So can we now shut up about banning advertising, refusing permission for fast-food shops near schools and a host of other irrelevances. The rise in obesity is down to a more sedantry lifestyle and that our energy intake hasn't declined as fast as our metabolic need for that energy.