Age of onset of puberty appears to be linked to a child's risk of obesity. Children born to mothers who experienced an early puberty are far more likely to be obese (via BBC).
If a woman had her first period before age 11, then she was 5 times more likely to be obese, and her children were 3 times more likely to be obese, than women whose first period was after age 15.
Age at menarche (first period) is something that seems to be inherited.
"Age at menarche is strongly related to your weight and it's well recognised that it's getting earlier and earlier." But she said that environmental factors were just as important as genetics.
Previous research has linked breastfeeding with lower rates of childhood obesity. However a new study of 35,000 nurses fails to find a similar link with adult obesity.