Since four of Alfred Lemon and Madie's children were born in Arkansas, I checked the 1900 Arkansas census for Madie and Alfred's families, before their marriage. And I found them!

Please see 1900- Madison, St. Francis, Arkansas, page 7 of 28:

Leman WEAVER, head, single, born Mar 1877, N. Carolina, farmer
Sallie WEAVER, mother, widowed, born Dec. 1858, N. Carolina
Bettie WEAVER, sister, single, born Sept 1883, N. Carolina
Dosia WEAVER, sister, single, born May 1887, N. Carolina
Robert McAILLER, ward, single, born April 1890, Arkansas
Arto McAILLER, ward, single, born Jan? 1892, Arkansas

And on page 13 of 28, the same census (the index says BENT not BURT):

Daniel F. BURT, head, married, born Nov 1854, Mississippi, father and mother born Alabama
Maggie BURT, wife, born Jun 1851, Mississippi, father born KY, mother born TN
Ward? BURT, son, single, born Aug 1876, born MS
Steven BURT, son, single, born Mar 1880, MS
Madie BURT, daughter, single, born Nov 1881, MS
Daniel F. P. BURT, son, single, born Oct 1883, MS
Lee BURT, son, born Feb 1885, MS
Lenobel BURT, daughter, born July 1888

In this Arkansas census, Maggie states that they have been married 23 years (1877) and have eight children, eight still alive. In the Mississippi marriage records, I found a possible marriage for Madie's parents:

10 August 1877, Carroll County, MS, Daniel BURT and Maggie WADLINGTON

In the 1910 and 1920 censuses Madie and Leman/Laymon/Lemon WEAVER/WEVER move to Luther, Oklahoma County, OK. and have at least eight children of their own:
Arthur, 1904
Magnolia /"Maggie", 1906
Olie, 1908
Sedalia, 1910
San Antonia, 1913
Forest, 1915
Birdie, 1917
Emmit, 1919

This should give you a good start on the BURT and WEAVER families. You have a lot of state records to look at - Arkansas, Alabama, Kentucky, Mississippi, North Carolina and Oklahoma!

Good luck,
Laura