Are you looking for James M. Weaver's first wife or his second wife, Sally (Hillen) Quinton? What clues do you have that makes you think they were from Newton County, Arkansas?
It appears from the 1900 Cherokee Nation, Indian Territory enumeration that James M. Waver was born ca 1860 in Arkansas and that Sally was born October 1874 also in Ark. Evidently his son Jasper Weaver, age 13 was by his first wife and that Sally had two children, Claud, 5, and Ida, 2 by a previous husband whose surname was QUINTON. Both of the Quinton children claim Indian Territory as their birth place, so it is quite possible that Sally (their mother) married James M. Weaver in Indian Territory also, ca 1900.
There are marriages for James M. WEAVER in the Index to Marriages, First U.S. Court, Northern District, Muskogee, Indian Territory, 1890-1907. One is to a Monta Shayheart, C-283 and the other to a Victoria Baker, C-197. ( do not have the exact dates. Since James Weaver is a rather common name, it is difficult to determine if either of these men are the one you seek.
If your primary interest is in James M. Weaver and his first wife, perhaps by following their purported son, Jasper Weaver, born ca 1887 in Arkansas, to see if you can learn more about him and where his parents were married and/or where he was born. First children were often born near the locality where their parents married in this time and locality.
I checked the few Newton County, Arkansas references I had and did not find a marriage for a James Weaver.