We have traveled the first week of September to the Caribbean for the last 30 years and have had two major storms that effected our stay.

Hurricane Earl (2010) brought winds of 120-135 MPH and shut down the island for a day and a half.
Royal Islander weathered the storm very, very well and ran on its sea generator

We were lucky to leave the island the day Irma (2017) hit cutting our vacation short. Many did not get so lucky and got stuck on the island for at least a week.

It is a humid time of the year, but other wise no problems with the weather.

Yes, some of our restaurant choices are closed for vacation, but we stay 3 weeks and still don't eat at all restaurants on our long list.
Some restaurants do offer some discounted menus for the slow season.

Traffic is much better and there should be problem getting into any restaurant

The week of Irma is when we met Jerry who posted above I believe