Weidler rose through German single-seaters, becoming German Formula Three champion in 1985. He subsequently competed in the International Formula 3000 series in 1986 and 1988 without major success. In 1989 he entered ten Formula One Grands Prix with the Rial team, driving the Rial ARC2 powered by a Ford Cosworth DFR V8. The car was uncompetitive and Weidler failed to prequalify on most occasions; at the German Grand Prix he was excluded after receiving outside assistance during a session. At the Hungarian Grand Prix he managed to make it through prequalifying, but finished last in Saturday qualifying and was subsequently replaced by Pierre-Henri Raphanel.
With no Formula One prospects available, Weidler found a new competitive home in Japan, joining the Japanese Formula 3000 championship and the All Japan Sports Prototype Championship. He became a consistent front-runner in Japanese F3000, frequently battling with Kazuyoshi Hoshino, Ross Cheever, and others. His 1991 Japanese F3000 season with Team Nova produced a third-place championship finish, and his 1992 campaign with the same team had him leading the championship at the time he was forced to withdraw.
Weidler made his Le Mans debut in 1987 with Kremer Racing's Porsche 962C, sharing the car with Kris Nissen and Kunimitsu Takahashi — the entry did not finish. He returned in 1989 with the Mazdaspeed team in a Mazda 767, finishing third in the GTP class. In 1990, now in the Mazda 787, he retired again.
The 1991 race defined his career. Paired with Johnny Herbert and Bertrand Gachot in the Mazda 787B, Weidler co-drove the car to outright victory at the 24 Hours of Le Mans, completing 362 laps. The win was the first by a Japanese manufacturer at Le Mans, the first by a Japanese engine, and — uniquely — was achieved with a rotary Wankel engine, a configuration noted for its extraordinary sound at racing speeds. Weidler returned in 1992 in the Mazda MXR-01, again with Herbert and Gachot plus Maurizio Sandro Sala, finishing fourth.
The hours spent inside the famously loud Mazda are believed to have contributed to a lasting consequence. Weidler subsequently developed sensorineural hearing loss — a condition described in contemporary reports as tinnitus producing a constant ringing — which became severe enough to force him to abandon the 1992 Japanese F3000 season while leading the championship. Before leaving his Japanese team, Nova Engineering, Weidler recommended Heinz-Harald Frentzen as his successor.
Following his retirement from racing, Weidler returned to Germany and became managing director of Weidler, a building cleaning company owned by his family, based in Weinheim.