Weiss followed in his father's footsteps and started boxing in 1958. He represented Austria at the 1960 Summer Olympics in Rome and won his first round bout by outpointing the Indonesian Tiang Hok Oei. Weiss lost the second-bout to Alfonso Carbajo and thus, got eliminated. Four years later he competed once again in The Olympics at Tokyo, he lost his first-round bout against Tunisian Tamar Ben Hassan.