The baby is expanded to approximately fifty times his height, width and girth but it's explicitly stated that he retains his orginal mass. This means he will have the same volume as one hundred and twenty five thousand babies of his original size, but will weigh the same as before he was enlarged! That child is going to weigh much less than the volume of air he displaces. He's going to float away.
When Wayne and Diane are looking for the machine in the lab's storage room, the box next to her has "Ark of the Covenant - Top Secret" written on it.