There are 3 US Post Offices in Weston County serving a total of 1,874 residents equating to 625 residents per post office. It's estimated that approximately 2,991 packages are handled across the 3 county post offices annually. Weston County is a county located in the U.S. state of Wyoming. As of the 2010 census, the population was 7,208. Its county seat is Newcastle. It is west from the South Dakota state line."