People with sedentary lifestyles were common in the 1900s as well, well above the 1% of the population that suffered from obesity. People with sedentary lifestyles have also tended to have more access to food, again with no corresponding explosion in obesity.
Also, agricultural output is not directly related to human consumption, past some base. So again, there may be second order effects on known causes of obesity (food and exercise) but if those are already controlled for, we are only left with unknown factors.
Regarding altitude, they do mention in a future article that California seems to be an exception, but that may be explained by California's drinking water being in a separate watershed than surrounding states. I don't know enough geography to know if this is accurate or not.
Edit: here is the quote from III:
> It’s important to note that altitude itself doesn’t affect obesity directly. Instead, altitude is a proxy for how high an area is in the watershed, which is itself a proxy for how badly the local water supply is contaminated. This is why Mississippi is more obese than low-lying areas of California. In California the water supply hasn’t traveled nearly as far in its path to the ocean, and has traveled past fewer farms, highways, cities, and factories.