Babies born weighing less than 5 lbs. are considered premature. In most cases, this means they were born before the 36th week of pregnancy. During weeks 36 to 40, the baby rapidly gains body fat at a rate of at least 1/2 lb per week, according to the MayoClinic.com website. By the time a baby is full term, he usually weighs between 7 and 9 lbs.