We love September. Have had a trip planned all but I think 1 year for the last 16 years. We were evacuated once a couple days after we arrived. One of the storms closed the road to Hatteras Island, so we had to use our trip insurance for a refund, but found a rental in Nags Head last minute which was nice. We had one year that there was storm out at sea and it rained for pretty much the entire week, but not evacuated. Other than that, we've really lucked out. Have had a couple rainy/windy days, but nothing that impacted our entire week. So really, in probably 15 years, we've really only had 2 years that were crappy (one evacuation, one all week rain).
If you don't hit a storm, the weather is so great in September. It's warm, but not horrible. The crowds are low, as well as the prices. We just make sure to get the insurance if we're staying in a rental.