The size of egg is larger than sperm because the the sperm enters inside the egg and egg has to accommodate the sperm. And egg contains fats and nutrients in order to feed zygote in case of pregnancy.
The egg is much bigger because it contains the food store for a possible embryonic development.
Egg cells are larger than sperm cells because it has a food stored inside for fertilized egg. And it's not true that the egg is bigger because it is the actual baby that grows, the baby that grows is the sperm cell that enter the egg cell!