Weber joined the faculty of the Department of Materials Science and Engineering, University of California, Berkeley, first as Assistant in 1983, than Associate and since 2001 as Full Professor, and stayed there for 23 years, until he accepted in 2006 a call from the Fraunhofer society.
From July 2006 to December 2016, he was director of the Fraunhofer Institute for Solar Energy Systems (ISE) in Freiburg, Germany.
In addition to his position as Director of ISE, he held the Chair of Physics/Solar Energy at the Albert Ludwigs University of Freiburg.
[1] In 2002, Weber and colleagues founded the German Scholars Organization [de] (GSO), of which he remains president today.
[citation needed] In 2016, he ran unsuccessfully for the Free Democratic Party in the state elections in Baden-Württemberg in the electoral district Freiburg II.