I can say with full honesty that I have been on cruises on ships of that size where I never even felt the ship move the entire cruise. I have also been on cruises where we hit rough seas - and they do move, but not nearly as much as a smaller ship.
I cruised the North Sea (above England) in a 4,000-ton expedition ship and we were pretty sick most of the time, but I just sailed the same waters, same time of year on a Celebrity Solstice class (Silhouettte) and I barely felt the ship moving. I don't think anyone was seasick although those are notoriously some of the roughest waters in the world.
In the Caribbean in February you are preactically guaranteed you will have a very smooth cruise. Don't worry.
But DO buy some bonine just in case. Vulnerability to sea-sickness is something no one can predict. And first-timers tend to get sick more often than veterans just because they think about it so much. Veteran cruisers don't think about ship movement because they expect it, but first-time cruisers tend to focus on each little motion.
Hopefully you can enjoy any the movement of the ship as most veteran cruisers do.
Keep in mind that most of the world's most expensive ships; Seabourn, Silversea, Regent, etc, are much smaller than mainstream ships and people pay a lot more to sail on them. That means that even on smaller ships the movement couldn't be bad enough to affect most people negatively.
On a ship like Freedom (156,000-tons) you are practically on solid ground
. (not really, it can shake, but probably won't).