According to the study from St Michael's Hospital, Toronto, children whose parents have high levels of stress have a Body Mass Index, or BMI, about 2 per cent higher than those whose parents have low levels of stress.
Children with higher parental stress also gained weight at a 7 per cent higher rate during the study period than other children.
Those figures may sound low, said lead author Dr Ketan Shankardass, but they are significant because they are happening in children, whose bodies and eating and exercise habits are still developing.
If that weight gain continues and is compounded over a lifetime, it could lead to serious obesity and health issues.
Shankardass studied data collected during the Children's Health Study, one of the largest and most comprehensive investigations into the long-term effects of air pollution on the respiratory health of children.
The childrens' BMI was calculated each year. Their parents were given a questionnaire to measure their perceived psychological stress.
Shankardass believes this is the first study to link parental stress to weight gain in such young children, adding it was not clear why the link between stress and obesity exists.
He said parents could change their behaviour when they are stressed, to reduce the amount of physical activity in the household or increase the amount of unhealthy food available.
Parental stress could also create stress for thechildren, who cope by eating more or exercising less, or whose stress leads to biological changes that cause weight gain, he said.
"Childhood is a time when we develop inter-connected habits related to how we deal with stress, how we eat and how active we are," Shankardass said.
"It's a time when we might be doing irreversible damage or damage that is very hard to change later," said Shankardass.
Shankardass noted that more than half the students followed in the California study were Hispanic, and that the effects of stress on their BMI was greater than children of other ethnic backgrounds.
The study was published in the journal Pediatric Obesity.