CaroleW, here's an update of information following your help.
I have looked at the handwritten announcement of Catherine's marriage to Robert Harvey and see it was witnessed by Andrew Murray Smith. A eureka moment! Lockhart Baillie's name was first found in a family Bible in the middle of a long list of......Smiths. One of them is Andrew Smith born later in 1811 so Andrew was a Smith family name.I think it's likely that Catherine, a farmer's daughter from Belhelvie went to the Borders to work, possibly in Mellerstain House, the almost-new home of George Baillie. She became pregnant by George, then 36 and unmarried, and had Lockhart in Kelso in 1799. On her own and far from Aberdeenshire she probably went home and the baby was brought up by Smith relatives. Seems a likely scenario.
Mellerstain is a Robert Adam mansion six miles from Kelso and would have been about ten years old then. It's still the Baillie-Hamilton family home and is open to the public. (There's a website.)
We've got this far by following up information you took the trouble to find - thankyou again.
