When Grant County was formed in 1820, William Arnold offered land for the county seat. Arnold was a veteran of the Revolutionary War and settled the area in 1795. The town built there was named after him when it incorporated in 1825.
The county grew slowly, reaching a population of just 281 by 1870. The Cincinnati Southern Railroad was built through the county in 1877, and Williamstown Lake was created in 1957. Finally, I-75 was built in the 1960s.
As of the census of 2000, there were 3,227 people, 1,279 households, and 879 families residing in the city. The population density was 202.2 people per square mile (78.1/km²). There were 1,375 housing units at an average density of 86.2/sq mi (33.3/km²). The racial makeup of the city was 97.95% White, 0.06% African American, 0.12% Native American, 0.43% Asian, 0.22% Pacific Islander, 0.81% from other races, and 0.40% from two or more races. Hispanic or Latino of any race were 1.46% of the population.
There were 1,279 households out of which 32.0% had children under the age of 18 living with them, 52.3% were married couples living together, 13.1% had a female householder with no husband present, and 31.2% were non-families. 28.4% of all households were made up of individuals and 15.9% had someone living alone who was 65 years of age or older. The average household size was 2.45 and the average family size was 2.98.
In the city the population was spread out with 25.8% under the age of 18, 8.5% from 18 to 24, 28.6% from 25 to 44, 20.4% from 45 to 64, and 16.6% who were 65 years of age or older. The median age was 35 years. For every 100 females there were 85.5 males. For every 100 females age 18 and over, there were 82.3 males.
The median income for a household in the city was $33,750, and the median income for a family was $44,808. Males had a median income of $31,466 versus $21,492 for females. The per capita income for the city was $17,945. About 10.9% of families and 15.4% of the population were below the poverty line, including 16.1% of those under age 18 and 20.1% of those age 65 or over.