My three year old is constantly burping.

Children swallow air when eating and drinking all the time, it either passes into the lower digestive tract or is burped out. Burping is good, and has no clinical consequences, at the most it embarrasses you if you do it in public (like farting does). Do not be overly concern as it is kind of a normal to burp. Sometimes, it would just be the speed of food intake and eating habits.