A physically draining job should keep one somewhat fit and healthy, 
  after all. 

Not necessarily, ex a waiter or a sales person would be drained by the end of the day but that doesn't make them fit and healthy.

  Their children too, are obese - which really suggests that it's 
  more of a culture issue.

There is a premium on healthy food while inexpensive food are fatty. "Organic produce" is multi-billion dollar industry.

The not so expensive meat that is available are frozen and/or have hormones & preservatives.

If you live off of "Dollar menu" you can't expect to be healthy. Most of the homeless are obese.

If I'm perpetually hungry the chances are that I'll eat food that will take longer to digest and in turn make me hungry lesser times during the day.