According to the United States Census Bureau, the town has a total area of 0.37 square miles (0.96 km2), of which 0.32 square miles (0.83 km2) is land and 0.05 square miles (0.13 km2) is water.[8]
The Kanawha River, which cuts through the whole state of West Virginia, passes by Leon.
As of the census[10] of 2010, there were 158 people, 61 households, and 46 families living in the town. The population density was 493.8 inhabitants per square mile (190.7/km2). There were 77 housing units at an average density of 240.6 per square mile (92.9/km2). The racial makeup of the town was 98.1% White, 0.6% African American, and 1.3% from two or more races.
There were 61 households, of which 26.2% had children under the age of 18 living with them, 60.7% were married couples living together, 9.8% had a female householder with no husband present, 4.9% had a male householder with no wife present, and 24.6% were non-families. 21.3% of all households were made up of individuals, and 21.3% had someone living alone who was 65 years of age or older. The average household size was 2.59 and the average family size was 3.00.
The median age in the town was 43.6 years. 15.8% of residents were under the age of 18; 10.8% were between the ages of 18 and 24; 27.8% were from 25 to 44; 21% were from 45 to 64; and 24.7% were 65 years of age or older. The gender makeup of the town was 50.0% male and 50.0% female.
2000 census
As of the census[3] of 2000, there were 132 people, 60 households, and 40 families living in the town. The population density was 385.7 inhabitants per square mile (148.9/km2). There were 73 housing units at an average density of 213.3 per square mile (82.4/km2). The racial makeup of the town was 100.00% White. Hispanic or Latino of any race were 0.76% of the population.
There were 60 households, out of which 26.7% had children under the age of 18 living with them, 60.0% were married couples living together, 3.3% had a female householder with no husband present, and 33.3% were non-families. 33.3% of all households were made up of individuals, and 15.0% had someone living alone who was 65 years of age or older. The average household size was 2.20 and the average family size was 2.80.
In the town, the population was spread out, with 18.2% under the age of 18, 5.3% from 18 to 24, 28.0% from 25 to 44, 31.1% from 45 to 64, and 17.4% who were 65 years of age or older. The median age was 44 years. For every 100 females, there were 97.0 males. For every 100 females age 18 and over, there were 103.8 males.
The median income for a household in the town was $21,429, and the median income for a family was $27,500. Males had a median income of $30,313 versus $11,000 for females. The per capita income for the town was $11,381. There were 16.7% of families and 12.3% of the population living below the poverty line, including 9.4% of under eighteens and none of those over 64.