We were there Sept 1-6 2015. Labor Day was late (9/7) and our school started back up 9/8 that year. It was crazy how not crowded it was (although I think it has continued to get more crowded at all times of the year as each year passes...), but it was also unbearably hot and humid (90s with 90+% humidity, with temp "feels" in the 100s) and there was pretty much a guaranteed thunderstorm/downpour every afternoon (as a result, we never got to see the FoF parade at all that trip). We still had a wonderful time, but our pace and touring plans (and our kids) were really affected by the extreme weather compared to the trip we just took a few weeks ago where the temps were in the 80s with much lower humidity. There are lots of good strategies to handle and make the most of the weather at that time of the year, but if I had a choice I wouldn't go back at that time. Another thing to keep in mind is the higher possibility of tropical storms and hurricanes at that time of the year. I remember monitoring the movement of TS Erika right before we left on our trip, and obviously there was Irma last year.
For me, I'd definitely pick the first week of March.