"..Some of his children's baptismal records list him as a cotton weaver..."
What do the others records list for occupation?
Can you list the baptism records that you have, with location, dates, parents names, and fathers occupation.
Baptisms of children of John & Mary Garth in Rochdale:
George 1799 Blackwater St. Unitarian Chapel; abode Toad Lane
Nancy 1801 Blackwater St. Unit. Chapel; abode Toad Lane
Betty 1803 Union St. Wesleyan; abode Toad Lane; occupation cotton weaver
Isabella 1805 Blackwater St. Unit. Chapel; abode Toad Lane
Mary 1807 Blackwater St. Unit. Chapel; abode Rochdale
Reuben 1812 St. Stephen, Rochdale; born 1810
William 1812 St. Stephen, Rochdale; born 1812
Parents for all were John & Mary.
Was a change from Unitarian to Wesleyan Methodist, back to Unitarian , then to Church of England, likely in Rochdale in the first 2 decades of 19th century? Delving into history of Non-Conformist chapels in Rochdale may provide some clues. It may have been that the parents had different views on religion.
Burial 1806 St. Chad, Rochdale;
Isabella, a child of John Garth; abode Toad Lane; occupation footman.
Are we certain that parents of Reuben (born 1810, baptised 1812) and William (baptised 1812) were the same John & Mary? There was no information about abode or occupation. The different denomination raised a doubt in my mind.
There was another John & Mary Garth who had some children (including 2 more called Reuben) baptised at Shaw Chapel which was C. of E. A John Garth of Prestwich parish married Mary Taylor of Ashton-under-Lyne parish at St. Michael & All Angels, Ashton-u-Lyne 1811. Banns called at St. Mary, Oldham, "John Garth, this parish". I wondered if Reuben might have been born before the marriage.