In case you dont have Census access.
1841 Census
Kelloe, Durham
Mark Waters, 25, Coal Miner
Diana Waters, 20
Elizabeth Waters, 3
Ann Waters, 1
All born in County
1851 Mark is away from Home;
Dinah Wardle Waters 31
Ann Waters 10
Dinah Waters 8
Mary Waters 6
William Waters 4
Margaret Waters 1
1861 they are under WATTERS, in Northumberland;
Mark Watters 45 born Gateshead
Dinah Watters 41 born Stickton
William Watters 14
Margaret Watters 11
Sarah Watters 10
Eleanor Watters 1
Ann Button 20
Dinah Button 6/12
MARK Waters Baptised 5 Nov 1815, St Mary, Gateshead
Parents WILLIAM/ELIZABETH
Fathers Occp Pitman
(FreeREG)
William WATERS married Elizabeth LEIGHTON, 29 Oct 1814 same Church
(FreeREG)
I cant find anymore Children in Gateshead for William/Elizabeth so they may have moved.
Mark remaried 1874 to Hannah KIRTLEY