We have been 6 times in May. It weather varies very little.
There is usually a little shower in the afternoon. It lasts anywhere from 30 min to 2 hrs. That being said , we have had a few days when it has rained all day. Not very often though.
We have never had a problem with any insects other than sand fleas. They usually show up after the rain until the sun comes back out and dries the sand, and in the evening. Just keep a bottle of Cutters in your beach bag or spray your ankles and feet if you plan on walking the beach at night.