A baby's newborn weight only affects their development in the sense that if your baby is underweight, you might have specific concerns regarding a baby's growth.
Some babies are born premature, and they have extra nutritional needs that your pediatrician will help guide you through. If a baby is an extreme preemie, they might be discharged from the hospital on fortified breast milk, or they might be discharged on a special formula that provides extra calories.
Breast milk and formula both provide 20 kilocalories per ounce. Some babies need extra caloric needs. Some companies make special preemie formulas and some formulas with extra calories. Your pediatrician will help you figure out which special formula or fortified breast milk your baby will need.
All healthy, normal weight babies who are appropriate for gestational age will stay on either breast milk or cows' milk formula, which provides 20 kilocalories per ounce, until a doctor advises otherwise.