"and holding consumption constant" is the trick, ain't it? Works great if you want to lose a little weight later more than you want to eat another 500 calories now. Most people don't want that (me included, by revealed preference -- I'm over 300 lbs).

When people say that obesity goes with poverty, they're noting that virtually everyone eats until they are sated, and if you eat until you are sated with high-quality, expensive food, you will be far less likely to be overweight than if you eat until you are sated with low-quality, inexpensive food.