Born in Leith on Coburg Street, Heatly was educated at Leith Academy and began his diving career with Portobello Amateur Swimming Club. He was inspired to become a diver after watching Pete Desjardins dive at Port Seton. Heatly was eleven years old, and Desjardins asked to see him dive and gave him tips. By the age of thirteen Heatly had become the East of Scotland Champion, and he held this title until the outbreak of World War II in 1939. The outbreak of war put things on hold; however, Heatly became a record holder in the 440-yards and 880-yards during this time. Heatly studied engineering at the University of Edinburgh and continued to train with PASC. Heatly wanted to enlist; however, as he was doing well with his studies at University, he was advised to join the Officers' Training Corps instead. When he graduated from University, he was commissioned into the Royal Engineers, but before he could be posted, the war ended. Healty became an apprentice at Rosyth's Naval Dockyard; however, he kept up his training at the sports facilities nearby and became a Scottish Freestyle Champion in 1946, a title he kept until 1958. Heatly married Jean Hermiston in 1948; he ran the family business of heating and ventilation, and a building and construction company while competing internationally and raising his four children.
International competitions
At the 1948 Olympics, Heatly placed fifth in the platform and 13th in the springboard. At the 1950 British Empire Games in Auckland, New Zealand, he won a gold medal in the platform and a silver in the springboard. Heatly had been unable to practise for most of the five-week journey by ship to Auckland, except for one training session which took place in a U.S. base in Panama. At the 1952 Olympics, Heatly placed 12th in the platform and 16th in the springboard. At the 1954 Commonwealth Games in Vancouver, Canada, he won a gold in the springboard and a bronze in the platform. The same year he won a bronze in the platform at the European championships. At the 1958 Commonwealth Games in Cardiff, Wales, Heatley was appointed as captain and flagbearer for the Scotland Team. He won a gold medal in the platform, and retired from competitions after that.
Later life
Heatly became the Chairman of Commonwealth Games Council for Scotland, in 1967–1971, Chairman of the Scottish Sports Council,, in 1975–87, and Chairman of the Commonwealth Games Federation, in 1982–90. Heatly has a unique connection with the Commonwealth Games as he has consecutively attended seventeen games, from 1950 to 2014, in an official capacity as a competitor, organiser, Chairman of the Federation, as the Life Vice President of the Federation, team manager and Chef de Mission. Healty was also the President of Scottish Swimming on two separate occasions, Chairman of the British Swimming Federation, was a Councillor for the City of Edinburgh and was an integral part of the planning of the Royal Commonwealth Pool. He also served in many roles on both the European and World Technical Diving Committees from 1966 to 1988.
Heatly had four children by his first wife Jean, who was also known as Bertha; she died in 1979. He re-married Mae Cochrane; she was also a widower with four children of her own. Together Peter and Mae had twenty grandchildren; Mae died in 2003. Heatly was diagnosed with prostate cancer in the 1980s but lived with the disease for nearly thirty years before he died. His grandson James Heatly won a bronze medal in the 1 m springboard at the 2018 Commonwealth Games.