There are many forms of diabetes and a number can affect babies. There are some that only affect babies that are under around 6 months, neonatal diabetes. For some it will go away and never come back in which case they had transient neonatal diabetes, for others it is permanent. Then you have type 1 which can be diagnosed at any age.

On it's own, the baby being overweight but being born at a normal weight is not something that would lead to diabetes in a baby and unless the baby shows symptoms of diabetes doctors will not routinely test for it. Even in adults, although being overweight is associated with type 2 diabetes there has never been any study that shows that being overweight actually causes type 2 diabetes.

This may interest you:

http://www.diabeticconnect.com/discussions/17...

diabetes, especially diabetes in children so young is not usually caused by the baby being overweight. There are many factors that can cause type 1 diabetes. Doctors do check babies for diabetes when they are young. Part of the reason you are supposed to take your baby in for wellenss check ups every few months during the first year is so that the pediatrician can check the baby's weight and growth progression and catch anything that is out of the ordinary.

No they were the normal size of a healthy baby

If you are meaning can babies have diabetes when you say be effected by diabetes then yes because some of my friends were diagnosed "I think the youngest I know of is 3 months" that might not be right but I know babies can have diabetes and you could ask your doctor to check for diabetes