I think Mary was born Mary Hogg, but that her mother subsequently married someone called Weatherall/Weatherald, hence the two surnames occurring on the births of her children
Mary seems to be born in various places according to the census: Yorkshire, Stockton and Darlington.
I did find a baptism of a Mary Hogg in Darlington St. Cuthbert: 5 Feb 1838 Mary Hogg, of Darlington, daughter of Elizabeth Hogg, spinster, illegitimate
There is a marriage in Stockton in 1839 of an Elizabeth
Hogg to a James
Weatherall.
1841 census
Coxhoe, Co. Durham
HO 107/313/11/44/8
James Weatheral, 25, publican, N
Elizabeth do, 25, N
Thomas do, Ag Lab, N
Mary do, 3, Y 1851 Census
HO 107/2389/271/16
Black Hill, Co. Durham
James Weatherall, head, married, 36, engineman, Yorkshire, Appleton Wiske
Elizabeth do, wife, mar, 3?, Yorkshire ?Old Brough
Mary do, daur, u, 13, Durham DarlingtonJane do, daur, u, 10, do, Stockton
George do, son, u, 8, do, Quarrington Hill
James do, son, u, do Cassop
(all children apart from Mary have mother's maiden surname Hogg)
In 1861 they are living in North Bedburn as the
Weatherald family, minus Mary (now married to Samuel) but with the addition of Elizabeth, RG 9/3714/10/13
In 1871 they are in Elswick, Newcastle upon Tyne as
Weatherald and with them is their daughter
Mary aged 33 , married, a stone dresser's wife, born Darlington RG10/5076/63/8. Mary has clearly been enumerated twice, as she is also with Samuel and children in Wallsend!
In 1881 James Weatherald is widowed, living in Newcastle upon Tyne, occupation licenced victualler. This ties with his occupation in 1841.
In 1891 he's living at Chirton, only a couple of miles from Wallsend.