William grew up in New Hanover, North Carolina, but later moved to Georgetown, South Carolina.
(At least one historian, W.W. Sellers who is usually reliable, tells us that William's first wife was the widow of Nathaniel Miller, Famariah Atkinson Miller.  He further asserts that William's children, Wm Jr.,James, Ruth, Martha, and Mary, were born of Famariah.  This would seem to conflict with some other records and dates that we have and other researchers have dismissed this as misinformation.   We are including her name and the presumed year of their marriage, parenthetically, as a possibility to be considered.)
In 1778 William married Patience "Minsey" Harrelson and the consensus of researchers seems to indicate that it was by her that he sired seven children.   Patience brought to the marriage two sons of her previous marriage to William Lewis, Isaac and Joel Lewis.
William Norton II apparently served, at least for a brief time in 1777-78, in the North Carolina Militia and he contributed to the cause of the American Revolution in South Carolina by securing goods and services for the Army.   He was a bit old for soldiering, 37 years old (although his father, Jacob, seems to have marched with the musicians of the 1st North Carolina).  He had three brothers who served in the American military.
The Norton's were members of the Church of England before the Revolution and  William was active in the Methodist Society in the Church.  After the American Revolution, when the Church of England was temporarily out of business in the former English colonies, some of the leaders of the Methodist Society in the United States organized "The Methodist Episcopal Church" (Christmas 1784).  Some sources refer to William Norton as "Reverend" and he may have been ordained by the newly organized church.  William C. Stapleton indicates in his Norton Family History that William was one of the founders and patrons of a Norton Chapel (Methodist) near Green Sea in Horry County, SC.   There is no such church extant and we have not looked into the history of Methodism in Horry County, but this seems credible.   However, it is possible that Stapleton is confused for we know that a church that William helped start was Miller's Church in Mullins, Marion County, SC, and it is still there today. The Nortons in the Carolinas, Georgia, and Alabama, for generations to come, would usually be faithful members and supporters of the Methodist Episcopal Church, South (now The United Methodist Church).   Many Anglicans followed this same path, although the lion's share of leaders in the American Revolution remained loyal to the Anglican religious tradition and became members of the Protestant Episcopal Church.   Ironically, most Episcopalians in America had supported the Revolution, while John Wesley's Methodist Society had staunchly opposed it.   In the new United States, the Anglican Church still smelled too much like the English Establishment.
William died in Horry County in 1806 and Patience moved to Alabama with one of her sons,
Ref:    "Early Settlers of Barbour County" Vol. II, by Marie H. Godfrey,
Eufaula, p. 120
Sellers' "History of Marion County, SC," pp. 475-480
"Original Index Book, Revolutionary Claims Filed in SC," James McCall, ed. Janie Revill, Baltimore, 1969, p. 259
Proofs recorded by the Sons of the American Revolution, see file of member #115091(David L. Veal)
"Stub Entries to Indents issued in Payment of Claims Against South Carolina Growing Out of the Revolution," Books L - N,
ed A. S. Salley, Jr.
Historical Commission of South Carolina, 1910
N    514               N    917               N    185
Book  U               Book  B               Book  F
Will, Horry County, 1 Aug 1806, Box 6, bundle 3
Barbour County Original Records, Box 233a