it doesn't weaken their system directly.
however, it effectively removes all possible pathogens from the water, or almost all of them... so the fish are never exposed to them... ie. they never get the fish equivalent of a slight cold, so when the flu comes along, if it gets past the sterilizer, they can be more susceptible.
however, many feel this is a load of bunk, and i know many people who use them with no ill effects. i think the general feeling is, if you're doing everything else right, you won't need it, as there really won't be anything to sterilize... so it's kind of a bandaid.