The normal weight of a 6 week old baby really depends on a lot of things. The average weight is anywhere from 9 lb. 14 oz. to 11 lb. 14 oz. The rule of thumb is about 5oz per week of weight gain. But again this depends on weather your baby is breastfeed or formula fed. If you are concerned about his weight gain speak with your doctor to make sure he is growing correctly and getting enough. Also take note of his diapers are his diapers full etc. HTH.