Scale is a Scots dialect word which means spill, or rinse. (Mind ye dinnae scale that watter hen = Mind you don't spill that water lass.) It appears to be Scandinavian in origin, related to the Norwegian word skyll. meaning rinse.
Scots shares many words with Scandinavian languages, like kirk, and bairn (barn)
I read somewhere that this song was based on a Russian story.
"She continues: "However, the ballad is not known before 1790 and could have had its starting point in a later incident that took place in Russia at the court of Peter the Great in 1719, when Mary Hamilton, a beautiful young woman who was maid-of-honour to the Empress Catherine, was beheaded for infanticide in the Czar's presence. It is not improbable that there are reminiscences of both these historical events in the ballad narrative."

From here http://sangstories.webs.com/fourmaries.htm