The fact that Giles was used as a given name a generation or two later, I think there is a good chance Obedience's father was a Mr. Giles. Roots web; notes that a John Giles (b- 1688 Tuckahoe Creek, Henrico County, Virginia; D- 1760 Henrico County, VA) married an Unknown woman who was born in 1715 in Barbados. He later married a Mary Moseley b- 1694. His father is noted as William Giles (b-1650 in Henrico County, VA and mother, Bethany Knowles b- March, 1669 in Tuckahoe Creek, Henrico County.
The link below seems to confirm the Giles family tree on WikiTree (with the exception of the mother/father/children noted at the bottom of the link):
https://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=moseley1&id=I689
John Giles was born in 1688.[1]
Robert was born in 1704.
William Giles appears to have died young. His wife, unnamed in his will, is given the underage children until a specified age is reached. Based on the order of listing in the will William is first born, second is John, third is Mary, and fourth is Nicholas.
William Giles Will as posted in Henrico Co VA Wills, 1654-1737, Weisiger: 11 July 1692, William Giles of Varina Parish. All to dear wife, sole executrix. To son William 12 pence. To son John, daughter Mary, son Nicholas 12 pence each. Son William to wife until he's 16, Sons John and Nicholas until 17 or 16 if she marries.
3 Sep 1711, John Giles of Henrico carpenter to William Byrd of Charles City Co Esq, 20 lbs to [sic] tracts on upper and lower sides of Falling Crk on S/S James River. Formerly conveyed to sd William Byrd by William Giles and Bethaniah his wife 29 Mar 1683. Wit Isham Epes, Fran’s Epes Jr. Rec 1st Mon in Sept 1711. Henrico Co VA Deeds 1706-1737, Weisiger, p28
https://www.geni.com/people/John-Giles/6000000002006077433
http://wvrebel.0catch.com/GILES.HTML
Since the above note; I found 3 Giles' on the 1704 Virginia Rent Rolls:
John Giles - Isle of Wight County
John Giles - Parish of St. Peters & St. Paul (think this is in New Kent County)
Thomas Giles - Isle of Wight County
One of the three above more likely could be Obedience (Giles) Thweatt's father.
Latest details in John Giles profile are based on Ancestry.com info. below: Navigation Person OptionsCAVENDER GOSS GRAY 3CAVENDER GOSS GRAY 3FIND PERSON IN TREE
CavenderCTOOLS John Giles 1688–1760
BIRTH 1688 • Tuckahoe, Henrico, Virginia, United States
DEATH 1760 • Henrico, Virginia, USA
Birth 1688 • Tuckahoe, Henrico, Virginia, United States 2 Sources
Birth of Brother Nicholas Giles(1690–1781) 1690 • Henrico Parish, Virginia, USA
Death of Father William John Giles(1650–1694) 02 Apr 1694 • Varina Par, Henrico, Virginia, United States
Birth of Daughter Agnes Mary Giles(1710–1757) May 1710 • St. Michael's Parish, Bridgetown, Barbados, Caribbean Islands
Death of Mother Bethenia Knowles(1669–1711) 14 Feb 1711 • Henrico, Virginia, USA
Marriage 1711 • Henrico, Virginia, USA Mary Moseley (1694–1754)
Birth of Son Perrin Giles(1715–1788) 1715 • , Henrico, Virginia, USA
Birth of Daughter Arthur Giles(1725–1753) 1725 • Henrico, Virginia, United States
Birth of Son William Giles Col(1727–1793) 1727 • Henrico, Virginia, USA
Death of Brother William Giles(1686–1727) 04 Dec 1727 • Y, Somme, Picardie, France
Birth of Daughter Sarah Giles(1730–) 1730 • Henrico, VA, USA
Marriage 1730 • Henrico, Virginia, USA Mary Moseley (1694–1754)
Death of Sister Temperance Overton(1679–1730) 1730 • Cedarhill, Hanover, Virginia, USA
Birth of Son Nicholas Giles(1733–1781) 1733 • Henrico, Virginia
Birth of Daughter Martha Mary Giles(1740–) 1740 • Henrico, Virginia, United States
Death of Daughter Arthur Giles(1725–1753) 1753 • Amelia, Virginia, USA
Death of Wife Mary Moseley(1694–1754) 1754 • Chestrfield, Virginia, United States
Death of Daughter Agnes Mary Giles(1710–1757) 26 May 1757 • St Philips Church, Charleston, South Carolina, USA
Death of Sister Mary Giles(1686–1757) 1757 • Hanover, Virginia, USA
Death 1760 • Henrico, Virginia, USA
Sources
Ancestry Sources
Bristol, England, Select Church of England Parish Registers, 1720-1933
North America, Family Histories, 1500-2000
Other Sources Ancestry Family Trees
Parents
William John Giles 1650–1694
Bethenia Knowles 1669–1711
Spouse & Children
Mary Moseley 1694–1754
Agnes Mary Giles 1710–1757
Perrin Giles 1715–1788
Arthur Giles 1725–1753
William Giles Col 1727–1793
Sarah Giles 1730–
Nicholas Giles 1733–1781
Martha Mary Giles 1740–
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