He came from a family that encouraged his interest in music, being taken to the opera and concerts regularly. Originally an economist by training with degrees from Balliol College, Oxford and London School of Economics and ten years working in various banks and other organisations. He nevertheless became more and more involved with music, as a performer, such as clarinetist with The Oxcentrics, and latterly as an organiser.
Weindling started the Babel Label in 1994, which has since had over 70 releases ranging from Penny Rimbaud to Billy Jenkins to Polar Bear and Acoustic Ladyland. He is also a director of the Vortex Jazz Club and was instrumental in achieving the successful move of the club from Stoke Newington to the Dalston Culture House.
He has two brothers: Michael Weindling is Professor of Perinatal Medicine and Consultant Neonatologist, University of Liverpool and Paul Weindling is Professor of History of Medicine at Oxford Brookes University.