Victoria and Jacqueline
There is no baptism for Nichol and the only child I can find baptised to Thomas Weatherston and Agnes Johnston is James born 1819 who may be the one with Nicol in the 1841 census in Kelso. This James is hard to find after that.
However I think you are on the right track, Victoria.
Found a Thomas in Hume, Berwickshire in the 1841 aged 45 with poss children, Mary,20, Agnes 15 and Benjamin 17. Benjamin dies in Ayton in 1890s and mother is supposed to be Agnes Wilson, father Thomas Weatherston. But think this is in error and it should be Agnes Johnston. I would follow the other children to their deaths if you can to prove it. Mary has an illegitimate child Thomas b 1852 and is in Kelso in 1861. Agnes is in Kelso too in 1851 so they are moving that way.
I believe this is the Thomas who dies in Kelso in 1860 aged 68 and his death record is signed by
son Nicol of Old Graden - which is where your Nicol is in the 1861 census. I have tried to find this Thomas in 1851 but can't as yet! The death record gives his parents as Nicol Weatherston and Janet Fairbairn. I you can find him in 1851 you will get his place of birth but I am struggling.

Barbara