As a track specialist Werner Weckert had some consistent results at the Swiss national championships during the first half of the 1960s. Riding as an amateur, Weckert finished second in the pursuit in 1960, earning himself a place on the Olympic team. At the 1960 Roma Games he was part of the Swiss quartet that competed in the 4,000 metres team pursuit, but lost their first round heat to France. In 1961 and 1962 Weckert came third in the pursuit at the Swiss championships before turning professional, with him finishing second at the 1964 championships. A year later he also rode in the Tour de Suisse but abandoned the race during the second stage.