Hi Colleen
I think you'll find that the ones which say born in Paisley are the family you are looking for in 1861.
Beacon Street, Hartlepool 3700/112
William LOWTHER, Head, Mar, 35, Labr., Faceby
Susannah, wife, 36, Stranton
William, son, 11, Faceby
John, son, 8, Faceby
Matthew, son, 6, Faceby
Robert, son, 3, Church ?, Durham
Henry, son, 1, Hartlepool, Durham
Robert, brother, 33, Faceby
Cheers
Gina