To answer your question, I've been on that itinerary on the NCL Breakaway in March from NYC pre-Covid. Yes, you should be bringing a heavy jacket for 2 main reasons: 1. Your port of departure will be cold up until March. 2. You will have 2 Sea days that you might want to take a trip up to the buffet or do a walk around. As to Bermuda itself, the temperature isn't that bad in March, mild for New Englanders like myself between 60-70 Fahrenheit, I would recommend a light jacket but I actually didn't need one. Long pants like Khaki's, Chino's, or Jeans will be fine with a simple short sleeve shirt. If you find those temperatures too cool due to the climate you are coming from, I'd recommend adding a cardigan sweater to your luggage and day bag, they come in handy.
As to the weather, you're not in hurricane season, but rain is possible. February, like March, should be a calm month for winds, so a light umbrella should be enough to handle small rain squalls.