The reason prices are cheaper in early December is because it is typically a slow time for the cruise industry because it is in between Thanksgiving and the religious holidays in December. People are more involved with holiday planning, gift buying, etc. These are great bargains for cruisers.
Do not dwell on weather conditions. There is no significant difference and you simply cannot predict it anyway. Most of the time any rain is passing in nature and won't last long. Also, if they can, the bridge will steer the ship around any rain if there is something with importance happening on deck. For example, last December on the Rock Legends cruise to Nassau we had a band playing poolside and storm clouds were looming. The ship managed to do some turns and slow down enough that the band (Artimus Pyle) could complete their last set.