Have you tried searching on familysearch.org?
You will be able to trace Thomas Rogers Norbury on there.
I have only looked at the Norbury side, but it is easy to find him.
Have you found the siblings of Thomas?
He had a sister Mary and a brother named Bradford.
You are very lucky in that the images of the birth and marriages at Stockport are directly linked to the names on familysearch. (This doesn't happen very often!). So you can see other information given if there is any.
For example, the baptisms of Thomas and his brother and sister give their father as a 'corn dealer' or 'corn chandler' of Market Street, Stockport.
There doesn't seem to be an Ann Norbury baptised as a sister.
If you then look for the birth of a James Norbury between, say, 1770 and 1790, there is one baptised in 1781 to Bradford Norbury and his wife Martha. This is surely the father of James, who has named one of his sons after his father.
And then you can find the marriage of Bradford and Martha in July 1769 at Stockport.
There is a baptism of an Ann Norbury to Bradford and Martha Dec 1769. This is at Disley just a few miles from Stockport. Again very luckily, this is directly linked to an image where it gives Bradford and MArtha as being 'of Norbury'. Norbury, the area, is part of Stockport, so it looks as if this may well be the same couple. Perhaps they went up to Disley to avoid people they knew in Stockport as the baby would have been born just 5 months after they were married.
So this Ann Norbury would have the aunt of James.
Surprisingly there seem to be several Bradford Norburys around at that time - some in the villages near to Stockport too. This may be from the way the entries at Stockport ST Mary's have been entered into the data base. I have an idea Stockport St Mary's was like a 'mother church', and entries from surrounding villages may well have ended up in their books as well. You would need to check this.
familysearch.org is always a very good place to start any research, and unlike other sites, it is all free. You just have to register for a free account. They have millions of films of parish registers, and as I said, you are very lucky that the entries for much of Cheshire are directly linked to the images in the actual parish registers.
Good luck!