I have lived here in the T&C for over 15 years so maybe I can help. September as a general rule tends to be busiest regarding hurricanes (and the hottest and most humid month of the year). For the most part, we usually don't have lots of rain in the fall, unless some crazy weather front moves in from the US. We do get afternoon or occasional showers but here, rain lasts 15 minutes and moves onwards and many times it can be pouring 2 miles away and clear sunny skies are all around. Basically the rain doesn't last. Have we had rainy weeks in the past during oct/nov? yes, but no more than any other month of the year.
I love the late october/november months here personally. It's just cooling off (and by that I mean not icky hot, it's a nice temp) and perfect weather during that time but the water is still warm for great swimming and the water tends to still be as a general rule really calm and flat. The winter months will bring some stronger winds and a higher chance of choppy seas. The island itself is much quieter, with hotels generally getting ready for the "season" and airfare is also better as well.
If you're looking at Oct/Nov, I would go more towards late oct vs early and anytime in November. We have been known to have a hurricane come through during those times but really that's rare vs September which always seems to see us boarding up for something.
Hope that helps