Snacking all day and night

My DS is 13.5 wks old. He snacks all day and night. His usual daytime routine is he gets up from a nap, diaper change, plays, eats 2oz then stays up til he is tired and will eat about 2-3oz until he falls asleep. Sometimes he will wake fromsleep (especially at night) whine for a bottle, eat an oz and then fall back asleep. This continues from 130am until he awakes at 7am-every hr or two. His pedi said he possibly snacks like this bc his tummy may not be able to handle more than 2oz at a time, but at this age I feel like he should be eating a full bottle at once. He also needs it to fall asleep and I need to break that habit...help! He currently sleeps in our bed and we are trying to change him over to his crib. We started with naps and now am going to start at night. He just finished a wonder week so thought this was a good time. Is he too young to CIO?