Mary could be the child of either Margaret STARR or Mary BECK, but probably the latter.

1a.  Anon.  1966.  Marriage Index:  Ohio, 1789-1850.  Liahona Research, Orem, UT (Broderbund CD-400):

Moreheart, Josiah

Starr, Margaret

Nov 29, 1838

Hancock Co.

1b.  Jordan R. Dodd, ed.  1998.  Marriage Index: Ohio, 1851-1900.  Liahona Research, Orem, UT (Broderbund CD-236):

Morehart, Josiah

Beck, Mary

Dec 25, 1851

Hancock Co.

2.  Family Quest Archives:  Ohio Federal Census 1840:  Hancock and Hardin Counties.  Heritage Quest CD M704-401:

1840

OH

Hancock Co.

Amanda Twp.

p. 50A

Josiah Morehart

100 010 - 000 010

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= William (b. 1839/40)
1 male	20-29	1810-1820	= Josiah (b. 1817/8)
1 female	20-29	1810-1820	= Margaret (b. 1819/20)

3.  1850 Ohio Federal Census: Hancock and Hardin Counties.  Heritage Quest, Family Quest Archives CD M432-692:  Amanda Twp., Dist. 48, Hancock Co., OH, p. 466A, 83/83, enumerated 7 Sep 1850, official enumerated date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Josiah Morehart	32	m	farmer	800
Margaret	30	f
Wm.	10	m
Sabella	8	f
Elisabeth	6	f
Henry	4	m
Christina	3	f
John W.	1	m

The blank locations apparently indicate Ohio.  Living next door to Andrew MOREHART.  For additional neighbors, see this table. 

4.  1860 Ohio Federal Census:  Hancock County.  Heritage Quest, Family Quest Archives CD M653-982:  Amanda Twp., Hancock Co., OH, p. 203A, 98/94, enumerated 4 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Josiah Morehart	39	M	Farmer	3500	500	O
Polly      "	28	F				"
William    "	20	M	Farm Laborar			"
Elizabeth  "	17	F	Servant			"
Christina  "	14	F				"
Henry      "	12	M				"
Wesley     "	11	M				"
Mary E     "	8	F				"
Watkins L  "	5	M				"
Marion     "	2	M				"
Clarinda A "	11/12	F				"

The first five children are by Josiah's first wife, Margaret; the last four by Polly, though it's possible that Mary was Margaret's child.  There are some inconsistencies in the ages of the children between 1850 and 1860, in particular, Christina's and Henry's ages seem to have been switched in one or the other of the years.  For neighbors, see this table. 

5.  1870 Census Images (online at Ancestry.com; Image #18 of 38):  Vanlue P.O., Amanda Twp., Hancock Co., OH, p. 22B, PN 18, 125/125, enumerated 28 Jun 1870, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Morehart Josiah	48	M	W	Farmer	4000	900	Ohio
________ Hester	37	F	W				Do
________ William	29	M	W				Do
________ John W	19	M	W				Do
________ Lafayette	15	M	W				Do
________ Marion S	13	M	W				Do
________ Annie	10	F	W				Do
________ Laura L	8	F	W				Do
________ George	7	M	W				Do

George is Hester's son by her first husband, Andrew L. MOREHART.  They are living next door to Hester's next husband, Washington MOREHART. 

6a.  1880 Census Images (online at Ancestry.com; Image #1 of 31):  Village of Vanlue, Amanda Twp., Hancock Co., OH, p. 493A, PN 1, SD 1, ED 184, enumerated 1 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	10	11	13	24	25	26
1	1	Morehart Josiah	W	M	60			/		Retired Farmer	O	O	Pa
		________ Laura	W	F	18	Daughter	/			Keeping House	O	O	O

Hester and Josiah have separated; their divorce will not be final until September.

6b.  1880 United States Census and National Index (LDS Family History Resource File: CD-ROM Library):

Census Place: Findlay, Hancock, Ohio
Source: FHL Film 1255021; NARA Film T9-1021; Pg 592C
	Relation	Sex	Marr	Race	Age	Birthplace	Occupation	Fa	Mo
Henry WATKINS	Self	M	M	W	58	NY	Com. Laborer	--	HOL
Sarrah WATKINS	Wife	F	M	W	46	OH	Keeping House	PA	PA
Marilla E. WATKINS	Dau	F	S	W	18	OH	At Home	NY	OH
Hester MOREHART	Other	F	M	W	46	OH	Dress Maker	--	PA
George P. MOREHART	Other	M	S	W	18	OH	Laborer	OH	OH

George is Hester's son by her first husband, Andrew L. MOREHART.

7.  1890 Census:  the 1890 census population schedules were destroyed.

8.  1900 Census Index/Microfilm (online at Genealogy.com):  Amanda Twp., Hancock Co., OH, p. 26B, SN 12, SD 7, ED 48, enumerated 26 Jun 1900, official enumeration date 1 Jun 1900 (extracted by Diana Gale Matthiesen):

1900:  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	7	8	9	10	11	12	13	14	15	19	22	23	24	25	26	27	28
276	281	Snyder William	Head	W	M	Mar 1849	51	M	28			OH	PA	OH	Farmer	Y	Y	Y	O	F	F	165
		______ Elizabeth	Wife	W	F	Mar 1845	55	M	28	1	1	OH	OH	OH		Y	Y	Y
		______ Truman	Son	W	M	Nov 1878	21	S				OH	OH	OH	Farm Laborer	Y	Y	Y
		______ Morehart Josiah	F in Law	W	M	Dec 1821	78	D				OH	Unk	OH

9.  Nancy Straub Holben.  The Chrisman -- Holmes -- Straub & Welch Family Genealogy.  FamilyTreeMaker User Home Page.