— born in KY:
  7.  John WILLIAMS, b. 1832/3

— born in MO:
  8.  Cpl. Richard WILLIAMS, Jr., b. 1833/4
  9.  Robert Andrew WILLIAMS, b. 1833/4 
10.  Thomas Henry WILLIAMS, b. 29 Jul 1834, Glasgow, Howard Co., MO; d. 14 Mar 1897, Missouri City, Fort Bend Co., TX
11.  Charles WILLIAMS, b. 8 Mar 1838; d. 15 Apr 1863, bur. Mercer Co., MO

1.  Family Group Sheet by Betty Ann (Matthiesen) Cogliati and her grandmother, Maude Irene (Thompson) Rose.

2a.  Jordan R. Dodd, ed.  1993.  KY, NC, TN, VA, WV Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):  not found.

2b.  Catherine Lindsay Knorr.  1950.  Marriage Bonds and Ministers' Returns of Prince Edward County, Virginia, 1754-1810.  Self-published, Pine Bluff, AR (reprinted 1982 by Southern Historical Press, Easley, SC):  not found.

3.  Census Index:  U.S. Selected Counties, 1810 (Broderbund CD-313):  there are 15 Richard WILLIAMS'es in VA, but none in Prince Edward Co.

4.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):  there are over a dozen Richard WILLIAMS'es in VA, but none in Prince Edward Co.

5.  Census Index:  U.S. Selected Counties, 1830 (Broderbund CD-315):  there are 15 Richard WILLIAMS'es in Virginia, but none in Prince Edward Co.
At this point, Richard's numbers at this point ought to be:

201 000 100 - 001 101 000

6a.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  our subject should be in Livingston [now Mercer] Co., MO, with his brother Royal WILLIAMS, who is there, but Richard is not found, at least not as head-of-household.  Richard's numbers at this point should be:

142 010 010 - 010 020 100

6b.  1840 U.S. Census Index/Images (online at Ancestry.com):  these are all the Richard WILLIAMS'es indexed as being in Missouri in 1840:

1840	MO	Carroll	292	Richard E. Williams	210 001 000 - 011 001 000
1840	MO	Carroll	301	Richard Williams	000 010 000 - 000 010 000
1840	MO	Cooper	137	Richd Williams	000 200 001 - 000 020 001
1840	MO	Montgomery	200	Richard Williams	011 010 100 - 112 201 100
1840	MO	Pike	58	Richard Williams	021 100 100 - 111 101 000
1840	MO	Scott	39	Richard G Williams	000 010 001 - 000 010 010
1840	MO	Wayne	219	Richard Williams	000 001 000 - 100 110 000

Based on the numbers, none of the above is remotely our subject, so I guess we just have to accept that Richard was missed in the census.

7.  1850 U.S. Census Index/Images (online at Ancestry.com; Image #28 of 66):  District 56, Mercer Co., MO, p. 386B, 177/4, enumerated 26 Aug 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Richard Williams	63	M		Farmer	400	Virginia
Elizabeth	58	F				do
Royal	23	M		Farmer		do
Henreta	19	F				do
John	17	M		Farmer		Kentucky
Robert	16	M		Farmer		Mo
Thomas	16	M		Farmer		do
Richard	14	M				do
Charles	11	M				do
Henry Belcher	30	M		Farmer		Kentucky
Susan Belcher	30	F				Virginia
M A	19	F				Mo
[Harvey & Susan's six children]

"Henry" should be "Harvey"; Susan (WILLIAMS) BELCHER is our subjects' daughter.  I presume "M.A." is Harvey's sister.  Listed three households from James Henry THOMPSON & Angeline THAXTON, who are next to Angeline's parents, Benjamin D. THAXTON & Malinda L. GAULDING, who are two households from Richard's brother, Royal T. WILLIAMS & Delilah Sampson GAULDING. 

8.  U.S. Census, 1860:  Washington Twp., Mercer Co., MO, p. 194 (extracted by Doreen McGowan):

WILLIAMS, Richard	74	M	VA
________, E.	66	F	VA
________, John	27	M	KY
________, Charles	21	M	MO
BELCHER, M.J.	17	F	MO

Martha J. Belcher is their granddaughter (by daughter Susan).

9.  Family Quest Archives:  Missouri 1870 Census Index.  Heritage Quest ACD-0019:  not found. 

10.  1880 Census Images (online at Ancestry.com; Image #3 of 27):  Washington Twp., Mercer Co., MO, p. 139A, PN 3, SD 7, ED 231, enumerated 1 Jun 1880 (extracted by Diana Gale Matthiesen).  For an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data). 

1	2	3	4	5	6	8	11	13	24	25	26
18	18	Williams Elisab	W	F	92		/		VA	VA	VA
		Crocket? Mary	W	F	65	Daughter	/	Keeping House	VA	VA	VA

Elizabeth should be 86-88, not 92; age inflation appears to have set in.  Listed next to Elizabeth's son, Royal WILLIAMS, Jr.

11.  Hoover, Mrs. B.F. & Mrs. D. Hesler.  1965. Middlebury Cemetery, Mercer County, MO (online at the Mercer County MOGenWeb site):

WILLIAMS	Richard	____	7 Jun 1878	98y 4m 3d; stone is down
WILLIAMS	Elizabeth T.	___	26 Jan 1886	99y 9m 2d; wife of R.
WILLIAMS	Chas.	____	15 Apr 1863	25y 1m 7d; son of R. & E.T.

Richard's age here does not agree with his age in the censuses; he should have been 92 at death, not 98.  Ditto Elizabeth; she should have been 94, not 99.  This appears to be a case of "age inflation," which is a common phenomenon found by genealogists.  In mid-life, people (especially women) want to appear younger, so they shave a few years off their age.  As people become elderly, they become proud of how long they've lived and start padding their age.  We should take the census records over the tombstones as being both first-hand and contemporary and, thus, a more accurate reflection of their true ages.  A later birth date solves another problem:  If Elizabeth really had been born in 1786, then she would have been 52 years old when she birthed Charles, an extraordinary age to be having a child, even in our own time of good health and ample nutrition, much less back then.  I don't buy it.  A last birth at age 46 or 47 is much more reasonable, though still a stretch.

12.  Birthdate calculated using Ben Buckner's JavaScript Birthday Calculator.

Entered		Result
7 Jun 1878	3d 4m 98y	4 Feb 1780
26 Jan 1886	2d 9m 99y	24 Apr 1786
15 Apr 1863	7d 1m 25y	8 Mar 1838

13.  Emails from Art Daly, Doreen McGowan.

14.  Public Member Trees (online at Ancestry.com):  in particular, the "Hall Family Tree" submitted by Carol Mahoney.