The "Christmas winds" typically pick back up in early/mid December, which typically means brisker Northerly winds, less humidity, clearer skies and less frequent rain showers, etc. I believe this weather pattern tends to hold pretty firm through February, maybe even in to March.
We have to remember, obviously, that Thanksgiving is only an American holiday. Charter pricing and flight pricing from the states is likely to be higher around this time due to that, but I would expect things would be more of what you would expect for a typical "shoulder season" in the anchorages and on shore. I don't think this is a common time for Euro's or Canadians to get to the BVI.
Late November is tail end of hurricane season, pretty low, but not zero risk. The waters are also still warm, but you have breeze and it's not as hot and less mosquito's. Every time of year is a great time to go, as noted above, no matter your date, there are tradeoffs of cost, crowding, weather patterns, etc. Even if you pick just the right time of year, there is always still a chance it rains all week.
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