I think I have found their marriage ...
Lamberton Toll June 15 [1839]. Wm. Hall to Jane Peterson [sic] both of Lowick. Witnesses William White, Catrine Gutrie [Irregular Border Marriages, Vol 1, Marriages at Lamberton Toll 1833-1849 (c) NDFHS 1995]
These are transcriptions from Henry Collins' registers for Lamberton which you will find copies of at both Berwick and Woodhorn, I'm sure (but please check!).
Also, I am sure that there is some connection between these Pattersons and my own lines, several of which shuttle regularly between Norham/Shoreswood, Ancroft and Lowick. I have a tentative theory about Jane Patterson's family and her connection to my own that I would be embarrassed to front up before the experts here ... do either of you, RT Cosic and Menager, have a DNA test with Ancestry? It would be interesting to see if we connect that way and would embolden me with said theory :-)