My ggg grandfather from Lesmahagow married a J. Muir from Lesmahagow in Ontario, Canada, after he became a man.
I have never looked up their immigration records.
Perhaps they met on the boat coming over, or they met a a Fair in Ontario, I do not know.
There is an Ontario@rootsweb.com and others that if you ask might give you some clues as to whether your William Weir moved here. Look up Rootsweb Canada They might have lived in Toronto Area or York County Ontario at least to start.
Canada was not a Country until 1867, so an UpperCanada@rootsweb.com might be one to join and make a query.
Some of our extended family moved to Michigan where they farmed, likely on former Indian Land. I have met a cousin couple from there and tramped around where mine and their ancestors lived in York County Ontario Canada.