1.  Marriage Record:

2a.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #3 of 5):  Muskingum County Infirmary ["Poor House"], Zanesville, Muskingum Co., OH, Roll, p. 79C, PN 35, SD 7, ED 156, enumerated __ 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	9	22	23	24	25	26
___	___	Bain Elizabeth	W	F	44	/	/	/	Ohio	___	___
		Hamilton Lillie M	W	F	10	/			Ohio	___	Ohio
		________ Harry	W	M	4	/			Ohio	___	Ohio
		Bain Geo W	W	M	1	/			Ohio	___	Ohio

Lillie and Harry are apparently Elizabeth's children with Elisha HAMILTON.  Elizabeth's ex-husband, Greenberry BAIN, had remarried in 1877, so he would not be expected to be George's father.  The fact that George bears the surname of his mother at the time of his birth suggests he is illegitimate, with the father undeclared.

2b.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #26 of 30):  Washington Twp., Muskingum Co., OH, Roll T9_1054, p. 341B, PN 26, SD 7, ED 174, enumerated 23 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	11	13	20	24	25	26
227	227	Bane Elizabeth	W	F	35?		D	Keeping House		OH	OH	OH
		"  Lill	W	F	8	Dau			/	"	"	"
		"  Harry	W	M	4	Son				"	"	"

Elizabeth has managed to get enumerated twice, once before the apparent death of son, George, and once afterwards.  Or did she give him up for adoption?  This page is faded and barely readable.  The LDS has read her age as, "30," but the second digit apprears to be 5 or 8, not 0; however, the first digit is definitely, "3," so she's fibbing about her age (and Lillie's age is either incorrect here or in the other record).