The article doesn't make sense.
They say that childhood obesity doesn't necessarily lead to adult obesity, and that they need to focus on adults rather than children, but then they do the comparisons not of adult children and their adult parents, but of children to parents.
It's blindingly obvious that in a household where the adults (who provide and prepare the food) are overweight, the children are more likely to be overweight. What would be interesting is seeing how those behaviour patterns manifest when the children become adults.