"families assigned to an area where the majority of the population were obese or thin passed through changes in their physical form to conform to their new places of residence."
This part of your statement contradicts the question, because from the obvious the human body's configuration is rather subject to environment more than anything. Obesity is more generic than contagious, if you look at the Japanese they hardly get obese due to one or two reasons ranging from their diet and other stuff. So no matter how many obese people are introduced to that area it kind of changes nothing: the human physical structure is only about 15% subject to external factors, the rest is all about the internal inner-workings.
Al the same, I find this topic and observation to be an interesting one.