I flew from Indianapolis, Indiana to Oakland, California during the so-called storm of the century in 1993. It was not a hurricane, but it did feature hurricane-force winds, and it was truly huge.
I was scheduled to have a layover in Ohio (Cleveland, if I recall correctly). I believe the airport was closed, but in any event at least one of the two flights was cancelled. I was rerouted through Denver. I don't remember whether I was delayed; if so, it was not by much. I might even have arrived earlier than originally scheduled.
Since your flight is (I assume) direct, and forecasts do indicate that the hurricane will be on the southern part of the North Carolina coast on Friday, it's possible that your flight would take a westerly detour to avoid associated bad weather. Your flight also might be cancelled, in which case you might be accommodated with a connecting flight through another city.
A major risk comes from congestion in the airline's network, and in the US commercial air system as a whole, resulting from cancelled flights in the path of the storm. Many of these travelers will be competing for available seats on flights that aren't cancelled. As I remember the 1993 storm caused delays that lasted a couple of days longer than the storm did; I was lucky not to have been caught up in them.
Another time, I was flying to a funeral when my flight was cancelled because of bad weather. The delay caused me to miss the funeral, but the airline gladly agreed to waive the change fees for me to rebook the ticket a couple of weeks later (in part, no doubt, because it helped to reduce the congestion in their network). If your flight is cancelled or delayed, you also may be able to reschedule your trip without change fees.