The seas should be fine in January. No hurricanes to contend with.

We have done New Years Cruises down in the Bahamas and Eastern Caribbean and the weather was glorious, too hot to walk around for long,it never gets cold down there..... as to the seas.... well you are out of Hurricane season, but no one can promise,storms can happen at sea but the Caribbean is usually clear turquoise seas,very calm. If you get a storm it won't last for the entire time you're there anyway. If there is any serious weather they will take you out of the way,that's why they always warn you that your itinerary can change at the Captain's discretion.

We did the Caribbean a couple of years ago early Jan and the sea was very rolly (if thats a word)
Most islands are close together so the captain went very slow adding to the roll
I dont think it helped that the Caribbean went through one of its worst seasons for a long time and 6 out of the 12 islands we did where a wash out...Trips cancelled due to mud slides, Beaches washed away it was really bad.
My lasting memory will be siting on a sun lounger in Tortola watching the rain pour down and being as cold as if we were back in the UK

BTW We did it on OV

Also I should have asked- what size ship are you sailing on? - that has a great bearing on how much motion you will feel. When you are on the big ships with their stabilizers it makes a huge difference.

Leaving New York on the Exploere of the seas in november going down to Caribbean. How rough is it likely to be, or not. many thanks

we are on OV2

Well that ship has stabilizers and is not huge at 64,000 tons,but that should be a nice smooth ride.
The smallest ship I have sailed on is 77,000 tons but you really feel minimal movement. I think you'll have a great trip.
As you are going out to sea on the first evening you might notice some motion,but after that you don't as a rule. The best thing about the CAribbean is that the weather is very even all year round, they just have two seasons wet and dry,and you will be in the dry season. It is popular for that reason- there is nothing like the Bay of Biscay down there.