The findings point to an important target group for obesity prevention efforts.
The researchers at the Children's Hospital of Philadelphia and the University of Pennsylvania also say that efforts to prevent obesity should focus on children as young as four, which underlines the potential role of healthy foods developed specifically for children.
The International Obesity TaskForce (IOTF) warned last year that at least 155 million school-age children worldwide are overweight or obese, a growing problem that needs to be tackled now if more serious ailments such as type 2 diabetes or heart disease are to be avoided.
And the food industry is increasingly being asked to play a role in tackling this problem, with a number of countries investigating a restriction on advertising certain foods to children.
The US team followed 70 children over a six-year period, including 33 with overweight mothers and 37 with lean mothers.
During the first two years of age, weight and body composition differed little between the two groups. But those children whose mothers were overweight had greater overall weight by age four, and both greater weight and more body fat by age six, they write in the January issue of the American Journal of Clinical Nutrition (81, pp140-146).
"We found dramatic increases in body fat between ages three and six," said lead researcher Robert Berkowitz. "This suggests that some genes controlling body weight may become active during this period."
Among the low-risk group, only one of the 37 children was overweight, suggesting that genetic influences can protect against obesity as well as predisposing to it.
The only environmental influence apparent in the study was family income; lower income was associated with higher body weight, similar to the pattern found in adults.
The researchers found no genetic influence for the fathers' weight, possibly because the number of children studied was not large enough.
Co-author Virginia Stallings said the research has important implications for preventing obesity. "It points to an important target group - children whose mothers are overweight. There could be greater benefits to focusing intense prevention efforts toward these children, rather than to the entire pediatric population."
Furthermore, the fact that increased body weight at age four is followed by increased body fat at age six indicates that prevention efforts should begin by age four for overweight children of overweight mothers, the authors say.
"It is not necessary to wait to see increased body fat by age six if the child is already overweight," Dr Berkowitz said.