Which mammal has the largest change in size from birth to fully grown percentage wise?
@JM97 is correct.
According to National Geographic >>
The gestation period of a Red Kangaroo is 33 days and it's baby at birth weighs a mere 0.03 oz. To put it into a more precise perspective, on birth, the baby weighs 1/100,000 of an adult red kangaroo's weight.
Second place goes to the baby of a Giant Panda; at birth it weighs 3.2oz which is 1/900 of an adult giant panda's weight.