How much do you know about the U S Census?
This is NOT a Civil War topic, so I can't pursue much beyond this post. The 1890 census was destroyed, so it's hard to search for families in the 1880s and 1890s.

The 1900 census for Tipton County TN lists Walter Ballard, born July 1878, married to Martha E (age 19) during the past year. Tennessee records show that Walter married Lizzie Martin in Tipton County on Mar 8, 1900. In 1920 they are living in Greenwood, Poinsett County AR. Walter died in Woodruff County AR on Jan 29, 1930.

Walter's middle initial isn't clear; could be 'B' or 'R'. They live with his mother Becky F Wales, widowed, born May 1857. Last name could be Wallace or Wallis. Also in household are her children Arthur (born Sept 1886) and Livie M (born May 1895), listed on the census as Walter's (half) brother and sister. Arthur Ballard died Benton Harbor MI Oct 5, 1970.

One of the twins mentioned (Essie and Lessie) is said to have lived in Missouri.