Norris was born in Kirtons, Saint Philip, and first represented Barbados at the 1962 Central American and Caribbean Games in Kingston, Jamaica where he won silver in high jump with a jump of 1.98 metres. Three months later at the 1962 British Empire and Commonwealth Games in Perth, Western Australia, Norris won bronze in the high jump clearing the bar at . In doing so, he became the first athlete to win a bronze medal for Barbados and the first athlete to win a medal of any colour in a sport besides weightlifting for Barbados at the Commonwealth Games. The following year, Norris was part of the inaugural contingent to represent Barbados at the 1963 Pan American Games in São Paulo, Brazil. There he won one of the first medals for his country, bronze in high jump. In 1966, he repeated his performance of four year prior in taking the silver medal at the San Juan Central American and Caribbean Games in the high jump and the bronze in high jump at the Kingston British Empire and Commonwealth Games.