fatvegan

Sharing the same childhood environment did not contribute to the similarity of the body-mass index of twins later in life. We conclude that genetic influences on body-mass index are substantial, whereas the childhood environment has little or no influence. These findings corroborate and extend the results of earlier studies of twins and adoptees.

The body-mass index of twins who have been reared apart

Basically they are saying that parenting has virtually no impact on whether or not children will be obese. Although it is possible that twins reared apart are generally raised by similar sorts of parents. They might be raised by other family members or people from the same communities or physical areas. So there is still the possibility that parenting does play a role, but there isn't enough variation in the parenting styles here to pick it up. It's still pretty amazing though.