Shipboard:
Should be fine. Could be a little cool and breezy at times if a cold front should pass into the region. Otherwise it should be very pleasant with smooth seas and mild to warm days.
Ports:
Expect it to be warm and humid but not especially hot. Comfortable for the most part I would say.
For both I would pack a lightweight jacket and maybe a sweater for evenings. And I would take a rain poncho and umbrella as on any cruise. In the tropics it can rain at any minute but it usually moves out fast unless it's a tropical disturbance in nature.
Basically this is an excellent time of the year to cruise. Pack plenty of warm weather clothing along with the above referenced items.
Hope this helps!
CD