Born in Toronto to Polish-Jewish immigrants, Weinzweig began studying music at age 14 and decided to become a composer by age 19, according to the Canadian Press. He attended the University of Toronto and traveled to Rochester, New York in 1937 to enroll at the Eastman School of Music, which offered courses in 20th-century music which Weinzweig could not get at home.
He returned to Toronto the following year, according to the CP, with modernist ideas about melody, harmony and rhythm which he started conveying to his students at that city's Conservatory of Music, where he taught for most of the next two decades. Among his students were R. Murray Schafer and Harry Somers, two of Canada's most prominent composers today.
Weinzweig's Suite for Piano No. 1 (1939) and his Symphony (1940) were, according to The Canadian Encyclopedia, the first Canadian works to explore serialism as a technique. In 1941 he began composing for the National Film Board of Canada and the CBC, to which he contributed for about a decade. Thereafter he composed only concert music, mostly for chamber-sized ensembles rather than full orchestra.
Encouraging and promoting the performance of Canadian classical music — and by no means only his own — was a lifelong preoccupation for Weinzweig: He founded the League of Canadian Composers in 1951 and the Canadian Music Centre in 1959, the first institutions to make a mission of advocating for the work of the country's composers within its own borders.
"He is identified as the person who created the profession of composing in this country," his friend and former student David Jaeger told the CBC. "In many ways," said Jason van Eyk, Ontario regional director of the Canadian Music Centre, to the CP, "if it weren't for him, we wouldn't have the wealth of Canadian composers that we have now."
The CP notes that Weinzweig was often critical of Canada's large musical institutions, particularly the Toronto Symphony Orchestra and the CBC, for what he saw as lackluster support for native-born composers. The news service's obituary cites an audio clip from a 2002 meeting of CBC producers in which Weinzweig is heard to say, "I'm too old for nightmares, but I have this dream that somebody is going to discover a piano concerto that was written by Mozart at the age of two and when the CBC gets hold of this thing, that'll be the end of Canadian music for the next 10 years."