The heart is said to be around the size of a fist - when a baby is born, the tiny fist they can make with their hands would represent the size of their heart currently. As the heart develops and grows with the same speed as the rest of the body through childhood and puberty it is always in proportion.
You can find lost of useful and interesting information about the human heart and its developments at websites such as:
When someone becomes a parent their heart is said to grow in the sense they now have something of their own to care and look after. Their outlook on life changes and everything will now revolve around their child.