Or is it just safer to fly in the night before?
It is always wise to try and get to the port a day early. Too many things can happen. Despite this being my usual advice I did fly to MCO on the day of the cruise this past August. In that case the bad weather was there up to the day before the cruise (tropical storm that hung off the coast of Florida for days), so in the end I made a good choice. But risk-wise, flying down on the day of the cruise is not the best choice.
Don't assume the weather in North Carolina and Miami will be good. Other factors: even if it is pleasant on the day of your flight remember that your airplane is most likely coming from someplace else - and the someplace else may have weather delays. It has happened to me on numerous occasions - most recently in June at ATL. We had nice weather. The problem was our airplane was coming from New York and they had lousy weather and were delayed. No big deal since we were flying home from a cruise. But it could have been the other way around.