The report from Boston University School of Medicine also found that the fewest weight problems occur among children whose parents are "authoritative" - having high expectations for self control but respectful of a child's opinions and who set clear boundaries.
The study also found that children of parents who are permissive, defined as indulgent and without discipline, also have weight problems but not to the degree of the offspring of strict disciplinarians with low levels of sensitivity, the study said.
Researchers also found that children of neglectful mothers and fathers, those who are emotionally uninvolved with no set rules, fared about the same as kids raised by permissive parents.
The study covered 872 children who were part of a group enrolled at birth in 1991 in a U.S. government study and followed for a number of years.
"Among the four parenting styles, authoritarian parenting was associated with the highest risk of overweight among young children," concluded the study published in the June issue of "Pediatrics," the journal of the American Academy of Pediatrics.
"These results provide evidence that a strict environment lacking in emotional responsiveness is associated with an increased risk of childhood overweight," the study said.
It may be that strict parents have defined limits on when and what their children eat that could have a negative impact if not accompanied by warmth and sensitivity, it added.
"A parent who is relatively insensitive to the child's emotional needs and development may impose a structure, such as requiring that a child clean his or her plate, that results in learning to eat on the basis of external cues rather than internal cues," the report said.
In addition, if a parent demands that a child exercise, it may result in an aversion to exercise, it said.
And living in a home with high expectations for self control but little sensitivity can be stressful, it added, and overeating can become "a stress response."