My father’s mother was Gwen Stout Thompson and her father was Claude James Stout whose father was Jonothan Benjamin Stout whose father was James Madison Stout whose father was Jonothan Stout. All of these Stouts lived at least part of their lives in Madison County, Arkansas.
The Internet Surname Database shows the following as the origins of the Stout Surname:
This interesting name has two possible origins. The first and most likely being, a nickname for a powerful, heavily built man, deriving from the Medieval English "stout" itself coming from the Olde French "estout", meaning "stout" or "bold". … A second distinct possibility is that the name derives from the Olde English element "stut" meaning a rounded hill and given to one dwelling by this natural feature. …
Jonothan Stout was the purchaser of the Stout Family Bible and the author of the quote that opens the bible: This book was bought at Boones Grove. Washington County Arkansas price one dollar and fifty cents and when this you see Remember Me. Jonathan Stout.