June to mid-November sees a substantial reduction in the number of cruisers (mostly sailboats) in the Eastern Caribbean. Most boats are on the hard tied down for the hurricane season. A good number of the remaining boats, mostly full time liveaboards, move south to Grenada so that they are at the southern end of the hurricane zone and if necessary can flee to Trinidad which is 86 nm south of Grenada in the event of a storm.
Yes the weather is calm until mid-December in the middle of the Eastern Caribbean. In late December and January you have the "Christmas winds" and travel is a matter of waiting for a weather window.
Friends who have put their boat back in the water in July and August for a couple of weeks of cruising tell me the weather is great for sailing.
Good luck, enjoy your trip. You will find the most cruisers are the opposite time period, mid-November to early May.