Is it normal for my baby to gain weight slowly?

Yes: It really depends on what you term "slowly." there are standardized growth curves that most babies will follow, within reasonable variation, that your pediatrician uses to track your baby's growth patterns. As long as your baby grows generally along normal gaining patterns, things are probably good. Remember, growth often has slow and faster periods.

Yes: I wish there were a "maybe" answer i could choose! your pediatrician will be keeping track of your baby's weight, and will know if the weight gain is in the healthy range. Gaining too little weight can be a problem-- but so can gaining too much weight. Babies don't have to be big and round to be healthy.