Children under the age of 6 have become heavier since 1980, but the risk of being overweight has jumped most for babies under 6 months.
The findings, published in the journal Obesity, add to concerns by some that the growing number of children who are born heavy or gain weight quickly in early life are likelier to face future health problems, including obesity, diabetes, high blood pressure, and possibly asthma.
It may be time for mothers (or fathers) to give up the traditional idea that a fat baby is a healthy baby, said Dr Matthew Gillman, the study's senior author.
But Dr Gillman and others do say that parents should not panic if an infant is heavy.
In general, the study considered children to be overweight if they fell in the top 5% on a measure that divides a child's weight by height.
They were considered at risk of becoming overweight if they fell between the 85th and 95th percentile.