Weber's first major appearance was at the 2011 Alpine SkiingJunior World Championships in Crans-Montana, Switzerland. He finished 9th in the downhill, and 17th in the Super-G. Having claimed his first podium at Europa Cup level, Weber competed in the 2012 Alpine Skiing Junior World Championships in Roccaraso, Italy. He claimed the silver medal in the Downhill, just 9 hundredths of a second behind the winner, and followed that with a gold in the Super-G the following day, ahead of teammate Nils Mani. As a result of the World Junior victory, by rule the winner is invited to take part in the World Cup Finals in that discipline, and Weber made his World Cup debut in the Super-G in Schladming, finishing in 22nd place. Weber was also the reserve for Switzerland in the Team Event, though he didn't take part in the race. In the next two seasons, Weber was mainly concentrating on the Europa Cup, with just a few appearances in the 2013 and 2014World Cups, without scoring any points. He was however able to claim his first Europa Cup victory in his home race in Wengen in 2013. Two more appearances at the Junior Worlds did not bring any more medals, and in fact Weber missed the rest of the 2014 season after suffering an injury in the Super-G at the 2014 Junior Worlds in Jasná, Slovakia. 2014-15 was to be the first season where Weber would compete in the majority of the 2015 World Cup races. He claimed his first World Cup points in the downhill in Santa Caterina, finishing in 10th place. Weber also picked up his first career points in Super-G, with a 25th-place finish in Saalbach. Weber missed the start of the 2016 World Cup due to a knee injury suffered in pre-season training, however, Weber was back by the events in Val Gardena in mid-December. In his first World Cup race of the year Weber finished in 11th position in the Super-G, and the next day posted the 7th fastest intermediate time halfway through the downhill, before failing to finish. Courtesy of other skiers injuries and the result in the Super-G, Weber reached the top 30 in the World Cup Start List for the discipline. The races in Kitzbühel saw Weber claim points in Super-G, and his first career points in the Alpine Combined discipline. However, due to a race jury decision to cancel the famous downhill after 30 racers, Weber would have to wait another year to tackle the Streif for the first time.
