I would say I'm about 99.9% sure that
DCL has never cancelled a cruise due to weather. I think that in my obsessive-compulsive researching I would have discovered it if they have, but I have not, and I'm confident that they have not. They did cancel a cruise in December of 2002 becuse of the Norovirus outbreak.
There are occasionally severe delays in arrival/departure (well, depending on what you mean by severe). I think the worst that I've heard of with DCL is that passengers had to be bussed to either St. Pete or Ft. Lauderdale because the ship couldn't tie up at Port Canaveral. I'm also relatively sure that this has just happened the one time.
The ship is occasionally late getting back in to port due to things such as medical emergencies or equipment malfunction. Cruise lines deal with these types of things all of the time, and have plans to allow for them. I've never personally encountered a huge delay with DCL, but with other lines, they have people working at re-booking flights, getting lodging, etc., even for people who did not book their air through the cruise line. My understanding is that this is standard practice in the industry and I would assume that Disney would do it as well, if not better, than most.
As for sailing during hurricane season, we've gone every year for the past 5 between September and December and have only been diverted once, in October of 2000. I would say that on average, a ship is affected by weather maybe 3 or 4 times a year at most. Some years not at all. I like sailing in the fall mostly because the rates are low, but I like that the days are still long and the weather still warm. I also like the chance that something unusual will happen and we might go someplace unexpected. As long as you go into it with that frame of mind, it's not a big deal if something happens. The way I look at it, I'm still on vacation and still capable of having a good time in Key West as opposed to St. Maarten (the itinerary change we had in 2000). Flexibility and a good attitude are the keys to sailing during hurricane season, I think.