Hi Ali. Have we been in touch before? Your query rings a few bells for me. If we have corresponded before, the following will not be news to you, but it may interest other people on this forum.
A lot of surnames are common on both sides of the Scottish/English border - e.g. Armstrong, Graham, Elliot - but Grahamslaw is actually the name of a hamlet near Kelso, which is probably why the name is of great antiquity in Roxburghshire. The earliest mention of the name that I know of is WILLIAM GRYMSLAW of the parish of Minto, who in 1493 was accused of art and part of the treasonable bringing in of the English of Tynedale, who rustled 100 cows and oxen, 100 sheep, 20 horses and mares, and sundry utensils, furth of Minto. This was the heyday of the Border reivers, of course.
In 1604 a band of Turnbulls were indicted for the slaughter of William, James, John, Robert, Andrew and Thomas GRAHAMSLAW of Little Newton. It's a wonder there were any Grahamslaws left after that bit of ethnic cleansing!
On September 24th., 1710, Alexander GRAEMSLAW of Maxwellheugh, Kelso, was "dilated for bringing in cabbage to his house the last Lord's Day between sermons", and was cited to appear at the next meeting of the kirk session to be disciplined. He may have been a descendant of James GRAHAMSLAW, maltman, and Margaret Sheill, who were married in 1664 at Kelso.
I have loads of stories like this, but coming up to more recent times, another GRAHAMSLAW researcher has assured me that the Border families of that name all descend from one of the following couples:
1. Thomas GRAHAMSLAW and Isabella HALL of Kelso,
2. Ruther and Elspeth GRAHAMSLAW of Jedburgh,
3. William GRAHAMSLAW in Yetholm.
My own ancestors include a pair of 4 x great-grandparents in Kelso called John Stewart (b.1766) and Jean GRAHAMSLAW. I was stuck on Jean for ages until the fellow researcher I mentioned told me of a couple called John GRAHAMSLAW and Elspeth Aitken who were having children at Ednam, nr. Kelso, in the 1760s. As John Stewart and Jean GRAHAMSLAW called their 2nd son John and their 1st daughter Elspeth, I think these are my Jean's parents.
A problem in researching Borderers is that a lot of them didn't belong to the established Church of Scotland, preferring little nonconformist sects like the Secession Church, and these people often didn't bother to register births/baptisms etc. with the parish church authorities, so they are invisible in the official records.
Harry