Sydney has had a really humid Summer which has given me a number of problems with different papers. I keep all my gear in dehumidifier cabinets as I live about 500 metres from the Pacific. All my paper is stored in a couple of drawers in the original packaging. I don't use any rolls, fortunately.
I'm hunting around for a possible storage solution which lets me control the humidity. The dry cabinets might be OK for A4 but SA3 and A2 would be a challenge. I'm also assuming that paper should be stored flat and not on end.