Your child will grow into 2 more stages; a kid (9-years old) and a teenager (about 15 years old). Each stage change will take 2 years (240 days) to complete. When your child reaches the last stage it will stop growing. No matter how old your son (or daughter) is the child will never help you with any of the farm work. The child also does not ever marry any of the other residents in the valley.
From
http://www.fogu.com/hm6/ under "your child"