I have Stor(r)i/e(y)s from Shotts too. They crop up with all sorts of spellings, but for simplicity I'll use Storry just now. Most of this information comes from the Registers of Sasines.
Andrew Storry of Wester Braco and Paperthills was born around 1670-ish. I don't have his father's name but his mother must have been a Naismith because he had an uncle named Claud Naismith.
Andrew married Mary Clark and had eight known children, the youngest (I think) born in 1727: John, Claud, Elizabeth, Mary, unknown, Andrew of Paperthills, William of Badallan and Peter of Badallan. The eldest son was John Storry of Wester Braco. He married first, in 1736, Anna Cleland by whom he had a son, Andrew Storry of Wester Braco. By his second wife Elizabeth Howie, whom he married in 1748, he had five known children: unknown, John, Margaret, Joseph, and Mary, the youngest born in 1768.
Margaret married John Wilkie and they eventually became my great-great-great-grandparents. Mary married George Duncan, baker in Glasgow. John died unmarried and as far as I know so did Joseph, who was a baker in Airdrie.
In 1796 Joseph, Margaret and Mary inherited property in Airdrie from their father John Wilkie.
Joseph was served heir to his brother John in 1797, and the document says that John was the second and Joseph the third son of John Storry of Braco and Elizabeth Howie. I have no idea who the eldest son was or what became of him. Nor do I understand why John did not share the property in Airdrie inherited by his brother and sisters.
If any of this sounds familiar, please get in touch.