Jefferson Connection

Great Great Great Uncle Archie (1772-1844) married Lucy Eppes whose brother was John Wayles Eppes (tree below). This marriage provides one connection to Thomas Jefferson, since John Wayles Eppes married Maria Jefferson, youngest daughter of Thomas and Martha Jefferson.

But there are also two direct connections to Thomas Jefferson that do not depend on the sibling relationship between Lucy Eppes and John Wayles Eppes. 

• Both Lucy Eppes and Maria Jefferson were granddaughters of John Wayles (via different wives of John Wayles). Lucy's mother was born of the marriage between John Wayles and Elizabeth Lomax. And Maria Jefferson's mother Martha Wayles Jefferson was born of the marriage between John Wayles and Martha Eppes. So Lucy and Maria Jefferson were first cousins in virtue of a common grandfather (John Wayles).
• Additionally, both Lucy Eppes and Maria Jefferson are the great granddaughter of the father of Richard and Martha Eppes. So Lucy and Maria are also 2nd cousins by virtue of shared great grand parents (in the Eppes line).

Summary: The marriage between Archibald Thweatt and Lucy Eppes ties the Thweatt line to Thomas Jefferson in three different ways.