Why do human body proportions change as we grow and age? For instance, why isn't a baby just a smaller version of an adult?

This is known as allometry - the change in shape as size changes.  Many animals are subject to this (juveniles are not just miniture adults).

It's not always clear why this is, though it results from different parts growing at different rates (the brain vs the digestive system, for instance).

I can't find much info on the specifics of why for humans, but here's a cool article on Allometry: http://www.nature.com/scitable/knowledg … g-13228439