Most babies born at 40 weeks gestation weigh an average of 7.63 pounds, according to BabyCenter.com. A baby who isn't born until 41 weeks gestation weighs an average of 7.93 pounds, and one who makes it to 42 weeks gestation weighs an average of 8.12 pounds. A baby born at 38 weeks, on the other hand, weighs an average of 6.8 pounds, BabyCenter.com notes.