One of the hardest tasks for a parent was to try to get a picky eating child to eat healthy food, she said.
"We found that out of all demographic and dietary information that the thing that most related to BMI (body mass index) in children were parental feeding practices."
Keeping track of what kids were eating makes them less fussy because parents were varying their child's diet more.
"Also parents that allowed their child to help themselves to food in the cupboard, they were more likely to be fussy children.
"The more freedom the child has, the more likely they're going to be a fussy eater."
It was easy for parents to "give up" with a fussy eater and let them graze on what they wanted to fill them up, Dr Haszard said.
Surprisingly, the study, which involved about 1000 children, also found that parents who restricted food portions and stopped children from eating junk food more often had obese children.
"We don't know if parents who restrict what their children eat causes obesity," Dr Haszard said.
"There's been some experimental research that says children who are restricted at home, then go on to eat more when they're not in that restricted environment - but I think more probably it's more likely that a parent that has an overweight child is really concerned about their child's weight, they limit what their child is eating.
"That's very possibly a good thing."
She said they needed to wait to see the results of the study on the cause and effect of obesity.
Dr Hazsard's advice to parents of fussy eaters:
• Keep an eye on what your child is eating.
• Model good healthy eating behaviours.
• Teach children about healthy food.
• Provide a diet with a variety of different foods.