Four to Five Weeks In about a month's time a bulldog puppy's weight will more than double from birth to 3 to 5 pounds. Larger puppies will weigh a little more, smaller puppies a little less. However, the size of the puppy at birth will not always be an indication of how much weight the puppy will put on in a month. The puppy's appetite, ability to suckle, the quality of the mother's milk and the puppy's stamina all come into play as the puppy grows. At this age and weight, the puppy is walking around.