Many parents overlook their child's unhealthy weight because they believe it is normal, research suggests.
Data on 2,100 Australian children found 40% of parents with an overweight or underweight child had not spotted this.
Among children, the underweight were more likely to think of themselves as average than the overweight.
The University of Melbourne researchers said parents would not act to help their children gain or lose weight if they did not see the problem.
"We live in a society where being big is becoming far more common, and is seen as normal"
Child obesity is thought to be increasing fast in many countries, and experts are hunting for effective ways to intervene, both at school, and home.
The Australian research shows just how hard it could be to challenge parents' perceptions of their children.
The Melbourne researchers analysed the 2,100 children using both Body Mass Index and waist circumference, to try to establish which fell into the "underweight", "overweight" and "average" groups.
They then compared these results with the recorded perceptions of their parents.
In total 43% of parents of overweight or underweight children placed their child in the "average" bracket.
For overweight children alone, this rose to nearly half. Remarkably, a very small percentage of parents had even more extreme views, assessing an overweight child as underweight, or vice versa.
The parents of boys were less likely to make a correct assessment.
When the children themselves were asked, six out of 10 underweight girls and half of underweight boys did not assess their weight correctly.
Big society
Dr Pene Schmidt, who led the research, said: "Parents are more likely to take the necessary preventative actions if the perception of their child's weight - whether underweight or overweight - is correct."
Tam Fry, from the National Obesity Forum, said that the results were "unsurprising".
He said: "There was recent research in this country which showed that a similar proportion of health professionals were unable to make the distinction.
"We live in a society where being big is becoming far more common, and is seen as normal."
He said that it was hard for health visitors and doctors to intervene if they were likely to meet a hostile response from the parent.
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