Elias Thorsteinsson weighed 6 pounds, 11 ounces, when he was born in January 2010. That put him in the 25th percentile of U.S. babies, meaning 25% of babies were smaller than he was at birth. But he didn't gain weight as quickly as other infants and dropped to the 1st percentile on the pediatric growth chart when he was 6 months old. "We were freaking out," says his mother, Randi Stebbins, a lawyer in Santa Clara, Calif., who rented an infant scale to weigh him daily at home.

Elias gained weight rapidly once he started eating...