In 1999 the Institute of Medicine (IOM) did a massive research into medicinal marijuana. It was all government funded. Their studies showed inconclusive evidence backing the theory that smoking marijuana weakens the immune system. In other words, no it doesn't.

Smoke of course will irritate the sinus and the respiratory system. Smoking with an upper respiratory or sinus infection is not good. Vaporizing is better but still not beneficial. Refraining until you get well is the best, but hard to do sometimes!