Agree that our sedentary lifestyles are a significant contributing factor to obesity, but you have it backwards about portion sizes.
Calorie dense (palatable) foods trigger our the reward centers in our brain more than non-palatable foods, and actually make us more hungry. This is an evolved survival strategy.
If you look at hunter gatherer diets, they will eat huge portions of extremely high calorie foods when they are available (e.g. drinking whole glasses of honey). They don't put on a lot of weight because they are more active, and don't have daily access to high calorie foods.
This means that large portions (and by extension obesity) are caused by the easy availability and low cost of high calorie foods. Telling people to eat less doesn't work because the systems that trigger hunger and fat retention work at a subconscious level and are in general more powerful than the conscious mind. The food environment that we have built up around us is a bad one for human beings.
If you want to learn more about how our hunger and fat regulation systems work then I can highly recommend "The Hungry Brain" by Stephan Guyenet .
Yet the French have dramatically lower rates of obesity than the Americans, and recent increases in the French obesity rate are mostly due to Americanization / a drift from traditional French food culture.
I obviously don't have the data, but I think it's simply because meals are traditionally "sacred" in French culture (that is, you don't eat snacks in between meals) and because portion sizes are much, much smaller than the American equivalent.
Everything about the American food culture works to subtly distort your sense of what a sensible portion looks like. A Big Gulp is a grotesque amount of soda, but it seems almost parsimonious compared to a Double Gulp. It's almost like gaslighting - you're constantly being told that vastly excessive portions are the norm.
I've heard this a lot but never experienced it. Are portions smaller in NYC (which is the only place in the US I've visted much)?
French food culture values home cooking from fresh ingredients which I assume results in food with lower concentrations of processed sugar.
#63 - France
#69 - U.S.
Let's not throw our hands in the air and blame the quirks of evolutionary biology when there are clearly better examples to follow.
The overall rank of all countries by body mass index places the US at #9 and France at #43. 
Evolutionary psychology is fine for producing plausible-sounding explanations, but I have not yet heard a single case where it actually produced something of scientific value.
Sure, aeons of scarcity obviously made us like food. But as can be seen with this example, culture often plays a much bigger role.
This is crazy. What are we doing? Nobody chooses to be fat, except maybe sumo wrestlers and a few other strange outliers.
Rates vary from 3.2% (Japan) to 30.6%. The median value is somewhere around 13%. Clearly there is more at work than evolutionary biology/psychology.
Regarding evolution, I don't think we would like to have a few billion deaths to let our DNA "adapt"