I find packing a sweater is always good, sometimes the dining rooms are chilly no matter what time of year you are cruising. Day time temps should be nice and sunny. Even if you run into some rain, its usually for a short period of time and doesn't ruin the entire day.
We have done the Eastern Caribbean 3 times. One of those times was the roughest seas we have ever experienced and the other two were pretty rocky for the first day or so. On the first occasion, our steward said it was next to, if not the worst seas he had been on. The stewards were going room to room handing out Meclazine, and there were barf bags on each stair case. The pool and hot tubs were closed down and drained as they had mini tsunamis drenching everything. Much better after a couple days. Don't want to discourage you though. Hopefully this was an exception, but I think we have had rougher seas on the Eastern runs than anywhere else. Come prepared, take something for nausea before sailing as it will be your first day out that will be the 'wooziest'.
Weather does tend to be cooler (although may not be for you) than a Western, especially the first couple days until you get well down into the islands. I have yet to leave Ft Lauderdale without needing a light jacket or sweater for sail away. Have a wonderful cruise. First cruises are wonderful and the addiction begins!