Of course premies have weak immune systems, their bodies didn't have time enough to build a strong immune system. I have a son who is 3 years old, and he was born 3 months early. He is as healthy as they come. If you are caring for a premie baby, don't worry if their immune system will build up, because it will. Of course you will have to be aware of the baby's surroundings.
premature babies do have weak immune systems but such is the case with all babies , that is why breast feeding is recommended as it has antibodies and nutrients which helps in developing the immune system. but as the babies grow older even the preemies , the immune system grows stronger and it does not affect them ( except in few cases which are very rare and are diagnosed immediately )