Most likely family as they are also in the 1880 census for Plymouth PA
1861 census RG9/3788 folio 106 page 32
Westoe, Borough of South Shields, Ward Jarrow, District Holy Trinity
No 5 Eldon Street
Thomas A.? Batey, Head, Mar, 46, Waterman, Northumberland Newcastle
Elizabeth Batey, Wife, Mar,40, Northumberland North Shields
Thomas Batey, Son, Unm, 18, Waterman, Northumberland North Shields
Mary Ellen Batey, Daur, Unm, 20, Northumberland North Shields
Ann Elizabeth Batey, Daur, 16, Scholar, Northumberland North Shields
Hannah Batey, Daur, 13, Scholar, Northumberland North Shields
George Wm. Batey, Son, 3, Durham West Hartlepool
Robina Batey, Daur, 1, Durham South Shields
West Hartlepool is in the Stockton registration district.
There is a marriage registered in Newcastle for a Thomas Batty and Elizabeth Bedford in 1844 Mar ¼ Newcastle Tyne 25 263, they married at All Saints Church. Getting their marriage cert will give both father's names. But first you must find out if this is your family. I suspect it is.
Janis