[2] It is home to the Museum of American Glass in West Virginia and the Trans-Allegheny Lunatic Asylum.

[7] Weston is the site of the former Trans-Allegheny Lunatic Asylum, a psychiatric hospital and National Historic Landmark which has been mostly vacant since its closure in 1994 upon its replacement by the nearby William R. Sharpe Jr. Hospital.

Jackson's Mill, a childhood home of Stonewall Jackson, is approximately four miles (6 km) north of Weston; it has been operated as a 4-H facility since the 1920s and is also the site of a conference center operated by the West Virginia University Extension Service.

Other buildings on the National Register of Historic Places are the Jonathan M. Bennett House and the former Weston Colored School.

The climate in this area is characterized by hot, humid summers and generally mild to cool winters.

There were 2,135 housing units at an average density of 1,094.9 per square mile (422.7/km2).

The racial makeup of the city was 97.0% White, 0.8% African American, 0.7% Asian, and 1.5% from two or more races.

33.7% of all households were made up of individuals, and 16.6% had someone living alone who was 65 years of age or older.

34.7% of all households were made up of individuals, and 18.6% had someone living alone who was 65 years of age or older.