A pool patio on Cove Hollow Road was given an okay by the East Hampton Town Zoning Board of Appeals on Nov. 19, but an adjoining pool house got an emphatic no. James and Christine Weinberg bought their half-acre property, which contained a 3,800-square-foot house, a 648-square-foot pool, and a 592-square-foot pool house, in 2002. The latter structure pre-existed zoning and was allowed to remain in place. The Weinbergs’ application, which was heard on Oct.