Feb 4th 2015, 18:41:57
vaccines work by introducing some element of a virus into our body so that our immune system identifies it and develops a memory for that part of the virus. That in turn lets our immune system recognize the virus if it gets into our body somehow in the future. So that can't weaken our system since it isn't getting rid of anything, only giving us a memory to recognize things in the future.
Now it may be that unless our bodies are exposed to the whole virus our immune system won't have a memory response to as many different things. But some is better than none when we're talking about diseases with serious complications.
CDC has information sheets for each vaccine. If you're that worried about it read up and then get your kids vaccinated.