Family Medical Care - Weirton Office. 3136 West Street, Weirton, WV 26062. 304-748-2828. Monday, Wednesday, Thursday & Friday - 8am to 4 pm. Tuesday 8 am to 6 pm. Every other Saturday - 8:30 am to 2 pm. Family Medical Care - Wintersville Office. 200 Luray Drive, Wintersville, OH 43953. 740-314-8258..