Hi Moggi,
I think this might be your family in 1841:
HO107/300/8/6/7
1841 Census: Eighton Banks, Chapelry of Lamesley, Durham.
Michael Rogerson/70/St. Quarryman.
Elizabeth Rogerson/70
Both born in the county.
On the same page:
Michael Rogerson/30/St[one] Quarryman.
Mary Rogerson/28
Elish? Rogerson [female]/3
Jane Rogerson/1
All born in the county.
HO107/296/12/32/18
1841 Census: Wrekenton?, Gateshead.
Philip Rogerson/44/Stone Mason
Elizabeth Rogerson/37
Elizabeth Rogerson/17
Michael Rogerson/14/Apprentice Stone Mason
Mary Rogerson/12
Philip Rogerson/6
John Rogerson/3
Joseph Rogerson/2/
All born in the county.
Hope it helps.
Jill