The newspaper "The Scotsman" recently went online from 1817 to 1900. There is an article that smells like it might be helpful. I did multiple searches based on information in your post and one article came up with both 'weir' and 'lanarkshire', that being a notice of sale of a 'valuable estate' in Lanarkshire appearing in the 25 Sep 1827 issue. I'm posting an informational note in this message board about the online resource, so if you're interested, please consult that message for information on how to reach the site.

Regards, Courtland
http://www.rootsweb.com/~archreg/vols/00009.html#0002115