Weeks worked all his broadcasting life with the BBC. Principally remembered for his commentary on winter sports such as ice skating and ice hockey, Weeks also presented swimming, snooker and gymnastics. Weeks was also a big speedway fan, and broadcast from Wembley Stadium on the World Speedway finals from 1955 to 1969 for the BBC. He reported for the BBC on every Winter Olympics from 1964 and most Summer Olympics until his retirement. As such he was on hand to describe the memorable gold medal wins of sports stars such as Olga Korbut, Mark Spitz, John Curry, Torvill and Dean and David Wilkie. For all this, he was affectionately nicknamed 'The Gold Medal Commentator' by his peers. Barry Davies took over his gymnastics duties in the Olympics, and Hamilton Bland in swimming. Davies and Weeks continued to commentate in ice-skating together, including the Torvill and Dean comeback at the 1994 Winter Olympics in Lillehammer, before a record audience of 23.9 million viewers in the UK on the BBC - a record audience for a non-football broadcast.
He made his last broadcast in early 1996 commentating at the World Figure Skating Championship. He then announced he was retiring, before he died in June that year.
His, to some, excessively enthusiastic style of presentation was sometimes parodied and satirised in the media. Once he read out in a loud, high-pitched voice the marks awarded by each individual judge for an ice skater. Clive James commented that Weeks was producing "television for the blind". Weeks defended himself by saying that it was a commentator's duty to get excited, and remained cordial towards detractors such as James.
He was also an occasional presenter of Match of the Day and commentated on football on the BBC for 20 years, including five World Cup final tournaments and Newcastle United's last trophy win, the second leg of the 1969 Fairs Cup Final against Ujpest Dozja. He occasionally presented Grandstand, and for many years presented the snooker series Pot Black.