William Alexander Weir was born on October 15, 1858, in Montreal, Quebec, brother of Robert Stanley Weir (1856-1926), a judge and author of the English lyrics for "O Canada."

He was a Quebec lawyer, politician, and judge. He was educated at the High School of Montreal, McGill University (B.C.L., 1881), and was called to the Bar of Quebec in 1881. He contributed articles to The Montreal Star (1880–1881) and the Argenteuil County News (1895–1897). Weir published several special editions of Quebec Civil Codes and served as Secretary of the Royal Commission to revise the Code of Civil Procedure in 1897. In 1897, Weir was elected a Member of the Legislative Assembly (MLA) for the riding of Argenteuil, representing the Liberal Party of Quebec until 1910. He also served as Minister without Portfolio (1903), Speaker (1905–1906), Minister of Public Works and Labour (1906–1907), and Provincial Treasurer (1907–1910). When he got appointed a judge for the Quebec Superior Court in 1910, Weir resigned his MLA seat. He finished his career becoming a Montreal District Court judge in 1923.

In 1885, he married Adelaide Jane Sayers Stewart (1865–1939). He died on October 22, 1929, in London, England.