Bate served in the Royal Australian Air Force during World War II. He studied at the University of Melbourne under Manning Clark, Max Crawford, Kathleen Fitzpatrick and John O'Brien. He taught at Brighton Grammar School, Melbourne Grammar School, Bradfield College (Berkshire), Monash and Melbourne universities. He taught at the University of Melbourne from 1953 to 1976. From 1978 until 1989 Bate held the foundation chair of Australian Studies at Deakin University, Geelong.
Bate was President of the Royal Historical Society of Victoria.
- A history of Brighton (1962)
- Lucky city: the first generation at Ballarat, 1851–1901 (1978)
- Dilemma at Westernport: a case study in land use conflicts and the growth of the planning imperative (1978, with Fay Marles)
- Private lives - public heritage: family snapshots as history (1986, with Euan McGillivray and Matthew Nickson)
- Victorian gold rushes (1988)
- Having a go: Bill Boyd’s Mallee (1989, with Bill Boyd)
- Light blue down-under: the history of Geelong Grammar School (1990)
- Life after gold: twentieth-century Ballarat (1993)
- Essential but unplanned: the story of Melbourne’s lanes (1994)
- Here’s to grandpa!: the watercolours 1900–1940 of C.A. Wilson (1995)
- Sustaining their dream: the Metropolitan Golf Club 1901–2001 (2001)
- Challenging traditions: a history of Melbourne Grammar (2002)
- Heads, you win!: a history of the Barwon Heads Golf Club (2007
- Pearce, Suzannah (2007). Who's who in Australia. Herald and Weekly Times. p. 211. ISBN 1740951301.
- "Heads, you win! : a history of the Barwon Heads Golf Club / Weston Bate". National Library of Australia. Retrieved 21 January 2013.