He has designed an electric-acoustic bass with an additional string tuned to C. Weber's music, often in a melancholic tone, frequently utilizes ostinatos, yet is highly organized in its colouring and attention to detail.

During this period, Weber also played and recorded with pianists Hampton Hawes and Mal Waldron, guitarists Baden Powell de Aquino and Joe Pass, The Mike Gibbs Orchestra, violinist Stephane Grappelli, and many others.

In the mid-1970s Weber formed his own group, Colours, with Charlie Mariano (soprano saxophone, flutes), Rainer Brüninghaus (piano, synthesizer) and Jon Christensen (drums).

Since the early 1980s, Weber has regularly collaborated with the British singer-songwriter Kate Bush, playing on four of her last six studio albums (The Dreaming, 1982; Hounds of Love, 1985; The Sensual World, 1989; Aerial, 2005).

On the occasion of his 65th birthday, in March, 2005 he recorded Stages of a Long Journey, a live concert with the Stuttgart Radio Symphony Orchestra and featuring Gary Burton, Wolfgang Dauner and Jan Garbarek.

With Gary Burton With Kate Bush With Jan Garbarek With Pat Metheny With Ralph Towner With Mal Waldron See "External Links" below for a complete discography Weber has, on at least five occasions, drawn on text from the book Watership Down (by Richard Adams) for the names of his compositions and albums.