I can now paint a little fuller picture of the lady I believe may be your great-grandmother Martha Sweeting:
1871 Framwellgate, Durham census
William Sweeting, head, 50, cart man, born Yorkshire
Martha Sweeting, wife, 37, born Durham
John Sweeting, son, 15, born Durham
Elizabeth Sweeting, daughter, 12, born Durham
William Sweeting, son, 9, born Durham
James Sweeting, son, 3, born Durham
Martha Sweeting, daughter, 1, born Durham
John Devlin married Martha Sweeting in the April-May-June quarter of 1887 in Middlesbrough (volume 9d, page 830).
1891 Middlesbro' census
John Devlin, 33, labourer, born Ireland
Martha Devlin, 26, born Durham
William Devlin, 3, born Middlesbourgh, Yorkshire
Catherine Devlin, 1, born Middlesbourgh, Yorkshire
John Devlin dies in 1899 or 1900 (looking at age in GRO) in Middlesbrough.
1901 Middlesbro' census
Martha Devlin, 37, widow, hawker, born Framlingate, Durham
William Devlin, 13, born Middlesbro'
Annie Devlin, 9, born Middlesbro'
Jane Devlin, 8, born Middlesbro'
Ellen Devlin, 6, born Middlesbro'
James Devlin, 4, born Middlesbro'
Robert Devlin, 1, born Middlesbro'
Martha Devlin marries Tom Hold in the Dec quarter of 1906 in Middlesbrough.
Thomas Hold died in the Dec quarter of 1909 at age 43 in Middlesbrough.
1911 Middlesbrough census
Martha Hold, head, 39, widow, married 4 years, 8 children living, 2 children deceased, born Durham City
James Devlin, son, 13, born Middlesbrough
Robert Devlin, son, 12, born Middlesbrough
Thomas Hold, son, 8, born Middlesbrough
Charles Hold, son, 6, born Middlesbrough
Martha Hold marries John W. Luthwaite in the Sept quarter of 1914 in Middlesbrough. (Martha's son William had two children with Sarah Jane Lewthwaite, in 1919 and 1921, at the time that Sarah was either divorced or widowed from Edward Cramner)
John W. Lewthwaite died in the June quarter of 1922 in Middlesbrough.
Martha Luthwaite married John W. Carter (yep, another John W.) in the Sept quarter of 1922 in Middlesbrough.
Martha Carter died in the March quarter of 1933 at age 62 in Middlesbrough. Her death is early in the year, so if she hadn't turned 63 yet, that would match her up with the Martha Sweeting who was born in the March quarter of 1870 in Durhan District of Co. Durham.A lot of folks never gave their correct age in the census, and that surely applies to Martha in the censuses prior to 1911.