Westwood is located at 39°2'18N, 94°36'56W (39.038305, -94.615583). According to the United States Census Bureau, the city has a total area of 1.0 km² (0.4 mi²), all land.
As of the census of 2000, there were 1,533 people, 711 households, and 418 families residing in the city. The population density was 1,479.7/km² (3,791.5/mi²). There were 731 housing units at an average density of 705.6/km² (1,808.0/mi²). The racial makeup of the city was 95.83% White, 0.33% African American, 0.26% Native American, 1.70% Asian, 0.91% from other races, and 0.98% from two or more races. Hispanic or Latino of any race were 5.09% of the population.
There were 711 households out of which 24.6% had children under the age of 18 living with them, 48.8% were married couples living together, 7.2% had a female householder with no husband present, and 41.1% were non-families. 35.3% of all households were made up of individuals and 12.2% had someone living alone who was 65 years of age or older. The average household size was 2.16 and the average family size was 2.82.
In the city the population was spread out with 20.5% under the age of 18, 4.2% from 18 to 24, 35.1% from 25 to 44, 22.8% from 45 to 64, and 17.3% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 88.8 males. For every 100 females age 18 and over, there were 83.7 males.
The median income for a household in the city was $49,185, and the median income for a family was $66,765. Males had a median income of $49,167 versus $35,898 for females. The per capita income for the city was $31,048. About 2.6% of families and 4.2% of the population were below the poverty line, including 6.2% of those under age 18 and 3.5% of those age 65 or over.