Weston is a city in Franklin County, Idaho, United States. The population was 511 at the 2020 census. It is part of the Logan, Utah-Idaho Metr…Weston is a city in Franklin County, Idaho, United States. The population was 511 at the 2020 census. It is part of the Logan, Utah-Idaho Metropolitan Statistical Area. It was first settled in 1865. The community was so named due to its location at the west bank of the Bear River.