Weston served as the first chancellor of the Order of Ontario, and she received the honour in 2001. She was appointed as a Member of the Order of Canada in 2003, and she had been invested as a Dame of Justice in the Venerable Order of St. John in 1997. She received the Canadian version of the Queen Elizabeth II Golden Jubilee Medal in 2002 and the Canadian version of the Queen Elizabeth II Diamond Jubilee Medal in 2012. In the 2015 Birthday Honours, she was made a Commander of the Royal Victorian Order.