But we've had abundance of food in the 20th century long before the obesity epidemic.

The US left subsistence farming behind around 1800 and had consistent surpluses ever since. You can see this in statistics of average height, they shoot up in the 1800's.

how "long"? Several studies have indicated (sorry, no sources) out that a person's diet during childhood affects the expressed genes of its offspring. There may be a generational lag (say, 20 years) between a change in diet and how it affects the population, it doesn't have to occur instantly.

We also had factory jobs, hands-on farm jobs, and plenty of other physical labor.