An anectdotal tale:
A friend of a friend has a little boy. When he was living with dad, he was a tad bit heavy, but not obese. He was active, and ate well. His mother decided to marry a man she knew for a month, and thus gained immediate custody for having an intact family (?) I shit you not, the judge felt this was more stable than being with dad who lived in the original family home!
Within months, this 8 year old boy gained over 30 pounds. I saw this myself, when he came over for a birthday party. He had stopped playing outside because he moved away from his friends, so he sat inside on the playstation all day. He ate oreos for lunch, and drank soda constantly. He became morbidly obese a short time after moving in with his mother. The poor kid was so fat that he couldn't run, and would trip on stairs all the time. He just was so sad.
Oh, and she divorced the new hubby 2 months after marrying him, but somehow the court did not see this as a problem.