There's a mildly awkward
Burials Weardale 1845 Ann Wearmouth abt 1831 St.Johns Chapel
but the above age matches the OP Ann and this one is a few years out from what we know so hopefully a diddy red herring.
Two possible other Anns
baptised March 1830, daughter of Robert & Margaret
baptised Jan 1831, daughter of Richard and Anne
More likely to be the latter - gravestone photo on Ancestry of Ann daughter of Richard and Elizabeth [??] buried Sept 1845 aged 15
The headstone inscription reads
Sacred to the memory of/ ANN DAUGHTER OF RICHARD/ AND ELIZABETH WEARMOUTH/ OF ST JOHN'S
CHAPEL WHO DIED/ SEPT. 27TH 1845 AGED 15 YEARS/ ALSO FRANCES THEIR DAUGHTER/ WHO DIED
MARCH 22ND 1864/ AGED 24 YEARS 11 MONTHS/ ALSO ELIZABETH THEIR DAUGHTER/ AND WIFE OF
GEORGE SANDERSON/ WHO DIED MAY 6TH 1867/ AGED 24 YEARS 5 MONTHS/ ALSO THE ABOVE
RICHARD WEARMOUTH/ WHO DIED DEC. 24TH 1875/ AGED 71 YEARS
There's also this Wearmouth headstone in SJC.
IN LOVING MEMORY OF/ RICHARD WEARMOUTH/ OF CHERRY TREE HOUSE/ DIED SEPTEMBER 8TH
1903/ AGED 72 YEARS/ MARGARET WEARMOUTH/ DIED MAY 21ST 1903/ AGED 63 YEARS/ JOHN
WEARMOUTH/ DIED JUNE 25TH 1853/ AGED 7 WEEKS/ MARY ANN JOHNSON/ DIED DECEMBER 26TH
1895/ AGED 41 YEARS/ MARGARET COULTHARD/ DIED SEPTEMBER 21ST 1883/ AGED 26 YEARS/ JOHN
WEARMOUTH/ DIED SEPTEMBER 30TH 1864/ AGED 14 WEEKS/ CHILDREN OF THE ABOVE/ RICHARD &
MARGARET WEARMOUTH/ ALSO/ JANE WEARMOUTH/ DAUGHTER OF THE ABOVE/ RICHARD &
MARGARET WEARMOUTH/ DIED FEBRUARY 16TH 1924/ AGED 62 YEARS
Burnfoot and Broken Way are both streets in SJC. Chesters refers to a pair of houses in SJC.
Anyone will tell you that Weardale family trees are notoriously difficult. Back in the mid 1800s there were only about 15 surnames in upper Weardale, first son's were usually named after their father, and eldest daughters often given their mother's maiden name as a middle name. Everyone was related somewhere along the line. My grandparents were Stobbs and Elliott and shared the same great grandparents who were also Stobbs and Elliott.
In addition, women were often still giving birth to children when they were already grandparents which often makes it hard to work out the generations.