Weigold is a world leader in experiments with electron beams incident on atoms and molecules. His work has had outstanding significance in investigating the mechanism of such reactions, in particular all aspects of the Coulomb three-body problem. He pioneered electron momentum spectroscopy, which is a probe of unprecedented power for electronic structure. It arises from his understanding of the mechanism of an (e,2e) coincidence experiment. A kinematic range can be found where the experiment directly observes spherically-averaged squares of momentum-space orbitals and critical aspects of many-electron wave functions.