1.  Jordan R. Dodd, ed.  1993.  North Carolina Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):  not found.

2.  1830 Census Images:  Randolph Co., NC (online at the Randolph County NCGenWeb site).

1830

NC

Randolph Co.

p. 65

J? Hopkins

000 001 - 100 001

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	30-39	1790-1800	= Joseph (b. 1806/7)
1 female	4 or under	1825-1830	= Rebecca (b. 1825/6)
1 female	30-39	1790-1800	= Rebecca

I have my doubts whether this is our subject.

3.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  not found, which very likely means our widower is living with kinfolk.

4.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  Southern Division, Randolph Co., NC, p. 154B, 1072/1084, enumerated 21 Oct 1850 (extracted by Diana Gale Matthiesen):

Joseph Hopkins	43	M	Farmer		NC
Rebecca   "	24	F			"
Whitson Russell	24	M	Farmer		"

Whitson RUSSELL is too old to be the son of Joseph's sister, Anna (HOPKINS) RUSSELL, but he is probably related somehow.  Listed between Joseph's father, Edward "Ned" HOPKINS, and Joseph's brother, Martin HOPKINS. 

5.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #155 of 177):  Ashboro P.O., Western Division, Randolph Co., NC, Roll M653_910, p. 216B/434, PN 156, 1164/1149, enumerated 14 Aug 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Jo. Hopkins	50	M		F.	600	840	NC
Rebecca  "	35	F		h.			"
Elieza   "	9	F					"

6.  1870 Census Index/Images (online at Genealogy.com; Image #17 of 28):  Burney Mill P.O., New Hope Twp., Randolph Co., NC, Roll 1156 (Book 1), p. 404A, PN 17, 135/142, enumerated 22 Sep 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Joseph Hopkins	62	M	W	Farmer	500	300	North Carolina
? Anna    "	20	F	W	Keeping house			"

7.  1880 Census (indexed at FamilySearch.org; page image online at Ancestry.com, Image #18 of 22):  New Hope Twp., Randolph Co., NC, p. 192B, PN 18, SD 2, ED 223, enumerated 24 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  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	9	11	13	24	25	26
191	200	Hopkins Joseph	W	M	69			/	Farmer	NC	MD	NC
		"    Elizabeth	W	F	50	House Keep	/		House Keeper	NC	NC	NC

Listed next to James HOPKINS (æ 36, b. NC, wife Louisa E.); and, in the other direction, listed five households from Joseph's brother, John HOPKINS, who is three households from their brother, Martin HOPKINS. 

8.  1890 Census:  the 1890 Census Population Schedules were destroyed.

9.  Anon.  2003.  The Heritage of Montgomery County, North Carolina.  Vol. III.  Montgomery County Historical Society (excerpt posted to the Hopkins Family Genealogy Forum, online at GenForum.com).  In Vol. III, on p. 384, is a biographical sketch of Benjamin HOPKINS, said here to be the father of our subject, but the article contains many obvious and serious errors, so caveat emptor!

... Edward “Ned” Hopkins was born in 1772, and in 1801 he married Hannah Crow...  Ned and Hannah had ten children... Joseph Alexander Hopkins was born in 1806 and married Rebecca Griffin...