CAN A BABY REALLY GET TOO MUCH MILK?       The mark of success at one time was to see how big and fat baby could be. It isn’t. It’s easy to mistake hunger for fussiness or crying from a tummy too full of milk or swallowed air. Yes, a baby really can get too much milk … that can result in irritability, vomiting, diarrhea, and eventually a fat baby. Be sure swallowed air is burped-up during, after and in-between feedings.