Since 2008 he has been competing in the SEAT León Eurocup, and he won the 2010 season with the Zengő-Dension Team.

He made his debut in the World Touring Car Championship in 2012 with Zengő Motorsport.

Wéber moved up to the 2012 season of the FIA World Touring Car Championship where he drove a BMW 320 TC for Zengő Motorsport alongside Norbert Michelisz.

[1] He was forced to miss the Race of Morocco due to financial issues and was only expected to compete in the European rounds of the championship as a result.

The Race of Portugal saw Wéber collide with Lukoil Racing driver Aleksei Dudukalo sending both cars into the gravel traps; they were able to return to the pits to retire their cars after the incident.