Black over Will's Mother's

Does anyone know the origin of the phrase
"It's a bit black over Will's Mother's (or Will's Mum's)"

It is usually used here in Sussex to describe the state of the sky when there is a storm brewing.

Eric Partridge, Dictionary of Catch Phrases: American and British, from the Sixteenth Century to the Present Day, has the variant ". . . Bill's mother's." "Applied to dark clouds looming--in no matter what quarters of the sky. The phrase is very common, later C20, in the East Midlands, but is by no means limited to that region, for I have heard it also from a Scotsman in Sussex, where also I heard the var. 'it's a bit brighter over . . .'"

Hmm. Where did Shakespeare's mother come from?