I've never seen a suggestion that it was anything other than a Scottish song, the words written by Donald Shaw, a weaver of Forfar with Chartist sympathies who published two collections of poems in the mid 19th century. He died, it appears, in 1856.

The onsite search engine here (you'll see it at the top of every page) will get you various references if you type work of the weavers into it. It's also spelled wark, but that won't much affect search results here.