Brown is a hugely popular name and produces a number of possibilities. Do you know Mary's maiden name? If not, it may be worth ordering the birth certificate of one of their children who were born after 1837 to find this out. There is a record of a Thomas Brown marrying a Mary Lisle at Tynemouth, which is next to North Shields, on 12 September 1835, which would fit with your timescales. However, there were others in Newcastle in 1831 and 1833 involving a Thomas Brown marrying a Mary so we are only guessing. My first port of call would be to establish Mary's maiden name.
Are you sure about the name of the village where Thomas was born in Roxburghshire? Could it have been Ancrum? I know the Ancestry transcription says he was 30 at the time of the 1851 census but it looks more like 50 to me. I know it was legal to do so then but it does seem unlikely that a 14 year old boy would be getting married in 1835. If I am right, that would make his birth sometime around 1801 and, coincidentally, there is the record of a baptism of a Thomas Brown in Ancrum on 23 August 1801 at Ancrum. Have you tried looking at the 1841 census to confirm this? It looks as if he was living in Cowpen, which is near Blyth and about 8 miles north of Tynemouth.
I leave the above with you as food for thought.
Regards
Gordon
