Prior to 1837 parents are not recorded on marriages (and only then father's) and 9 times out of 10 witnesses are unrelated.
I see from the census that Joseph Wheat bc.1805 (1806 in 1851 and 1804 in 1861). His birthplace is Thringstone, Leicestershire and this was a township in Whitwick parish.
This could well be his baptism:
Joseph Wayte bp.4/9/1803 St. John the Baptist, Whitwick, Leicestershire, son of John and Ann.
Likewise Elizabeth Atkin - census states bc.1806 Burton Joyce, Nottinghamshire - and would suggest this is her:
Elizabeth Adkin bp.12/9/1804 Burton Joyce, Notts. dau. of John and Martha.
Annette