Born in Scotland, he was the son of a builder, James Ross Weir. He was a pupil at Dollar Academy before moving with his family to London as a young man. He worked as a travelling salesman for a haberdashery company before he went into business on his own account in 1863 importing sewing machines. He retired from business in about 1879/80 to pursue politics full-time. Weir's brother, John Weir became the secretary of the Fife and Kinross Miners' Association.