I don't know too much about William Brigman after he moved to Anson, but I do know he lived in Richmond County before then. I have the following records in my notes.

1. This one shows who Margaret Brigman's father was:
1828: Richmond: Deed: NC, Book N, Page 92 John Mc D Shaw??? From Nancy Campbell and Others. Deed between William Brigman and Margaret his spouse, Nancy Campbell for Mary Hansel, Nepsy Sanders and Sarah Campbell Junior? Of the one part and John McD Shaw, $150, 100 a being granted to Colin Campbell deceased the 27 Nov 1793. Witness: Dill? McIntyre, Duncan McLaurin, Murdock Murphy, Peter Patterson, Archd C. Sinclair

2. This one indicates that William Brigman was the "son of Augustine Brigman's wife"...which is worded extremely strangely:
1825 NC: State vs. Wm. Beasley
[witnesses] Jesse Viner & Wm Brigman (son of Augustin Brigmans wife.)
Spring Term 1825
State of No Carolina
To the Sheriff of Richmond County Greeting
You are hereby Commanded to Summon Jesse Viner and Wm Brigman (son of Augustin Brigmans wife) and Delitha Woodle – personally to appear before the Judge of our Superior Court of Law to be held for the County of Richmond at Rockingham the Thursday after the 3d Monday of March next to give evidence in behalf of the state – in a Suit then and there pending where in the State & Delitha Woodle is plaintiff; and William Beasley is Defendant and this shall not be omitted under the penalty of Law. Witness B.H. Covington Clerk of the Law Court at office the 8h Monday of Sept 1824. B. H. Covington. (Transcribed from original at North Carolina Archives, Raleigh, Terri Brigman England.)

Augustine was the brother of Joshua Brigman who married Temperance Quick of Marlboro and moved to Walker County, Georgia in 1836. Joshua was born about 1780 and I believe (but can't prove) that Augustine was his older brother.

Augustine enjoyed knocking others in the head as shown by this record:

The State vs. Augustine Brigman and William Leviner, affray
John Crowson and James Terry: wit
State of North Carolina Richmond County
March Sessions 1803
The Jurors for the State upon their Oaths present that Augustine Brigman and William Leviner both late of the county of Richmond labourers on the 8th day of March AD 1803 with force and arms at the county of Richmond aforesaid in the public streets of Rockingham within said county in presence of divers good and peaceable citizens of this state did then and there commit an affray to the great terror and alarm of the said good and peaceable citizens of this State and against the peace and dignity of the State.
(Transcribed from original at North Carolina Archives, Raleigh, Terri Brigman England.)

Augustine and Joshua Brigman were the sons of Jacob Brigman as shown by the record below:

1836: Richmond:
Deed: Richmond: Page 414, 1836, DUNCAN MCNEILL? From JOSHUA BRIGMAN
“This Indenture made the thirteenth day of August 1833 between JOSHUA BRIGMAN of the County of R? and DUNCAN MACNEILL? Of same county…in consideration of three hundred and seventy five dollars to the JOSHUA BRIGMAN in hand paid…doth grant…a certain tract or parcel of land lying in the County of Richmond…as followith. The first Tract lies on the North East side of Joe’s Creek…containing 100 acres being the one half of a 200 acre tract granted to JOSHUA BRIGMAN decd in the year 1779 and conveyed by his son AUGUSTUS BRIGMAN by deed to his Bro JOSHUA BRIGMAN the 21 day of Nov 1801 which deed was proved March Sessions? 1805 and recroded March 22, 1805 in the Register’s Office Book F, Page 385. The second Tract contains 4 ½ acres (illegible) corner? Of his old tract North of Joe’s Creek in ISAAC WILLIAMSON’s line and runs the ? of I WILLIAMSON’s ?…granted to said JOSHUA BRIGMAN the 12th of Dec? 1821 containing altogether one hundred and four & a half acres of land and all houses buildings…Signed JOSHUA BRIGMAN

And another couple of miscellaneous records:

1821: Richmond:
Deed: NC, Book L, Page 374, Nathaniel Gibson to Augustine Brigman
$600, 250a, southside of Little Beaverdam, granted May 31, 1816 by deed from John E. Graham. Witness George Wright, Isaac Williamson, recorded April term 1821

1828: Anson:
Grant: William Brigman, land grant No 2959, Anson, 227 acres surveyed 27 Feb 1828, Book 138, Entry 993, Page 346, Chain bearers Mathew and John Griffin, Joining Elisah Stack nd Joshua Walter, Grant Issued 15 March 1830…”supposed to be in Hollamons line?….to the state line?….

Hope you find this of interest...

Cheers,
Terri Brigman England