Weymouth   South Shore vacationers want to detour through Weymouth, home of the Abigail Adams’ birthplace and some of Boston Harbor's best views.   The state’s second oldest community, Weymouth holds architectural gems like the Fogg Library. The community was once a military and industrial hub, housing a naval base, Stetson Shoe and the Nike Missile Base. All have undergone major transformations to retail, corporate and recreation uses, with the former missile base now enjoyed as Webb Memorial State Park.     Quick glimpse Municipal website: www.weymouth.ma.us Incorporated in 1635... located between Hingham Bay, Hingham, Braintree, Holbrook, Abington and Rockland...has a population of 55,000... and 21.61 square miles of land.