Which surname is it that you would like to find out about? Ainsworth or Weeks? Most of the folks are from the Chesterfield District in South Carolina beginning around 1740. The Ainsworth descendants migrated to Christian , Kentucky to Tennessee, and on into Mississippi abot the time of it's formation as a state. The Weeks mentioned in the book are from James Weeks, Sr. from Virginia in the 1700's. Some migrated into Georgia, and Franklin County, Tennessee and on into Mississippi. Most of these folks are of the southern descent. The books has mostly photographs and some information on these two families.
Please try to give me a little more detail and I'll let you know if I can help.