Chilmark is deep into openings and new beginnings. Most of the town businesses are either opening this weekend or next. The Chilmark Store will open May 10; The Bite and the Galley, both Menemsha eateries, will open May 16, with Beetlebung Café following on May 20. The Beach Plum Inn restaurant is open from Thursday through Sunday for the next couple of weeks, and the Home Port Restaurant will open on Memorial Day weekend.