A wide range of weights are considered ‘normal’ for a baby. You should be able to consult local healthcare professionals to keep track of your baby’s development, including weight, and they’ll alert you to any problems. Newborns are generally between 2.4kg and 4.2kg.
For older children, one-year-olds range from 7.8kg to 12kg, and two-year-olds 9.8kg to 14.7kg.
It’s worth bearing in mind that the first couple of years are not the time to be worrying about childhood obesity. By all means take care over what you’re feeding your child, and avoid refined sugar and fats and so on, but your child’s weight at this age has no bearing on their adult weight. Lots of heavy babies have gone on to have no trouble whatsoever with their weight in later life. You’ll often find that the chubbiness vanishes as they become more active.
It’s much more important that they have enough energy to grow properly and are getting all the nutrients they need to be healthy. Small babies in particular don’t know how to be greedy, they respond to what their body tells them, so if they demand to be fed it’s because their bodies are telling them to.