Born in Paterson, New Jersey, Weber graduated from the US Naval Academy in 1940 and served in the Navy until 1948, when he joined the faculty of the University of Maryland, College Park. He completed his doctorate at the Catholic University of America, Washington DC, in 1951 and was appointed professor of physics at Maryland in 1959, a post which he held for the remainder of his career.

Einstein's general theory of relativity predicts that accelerated masses should radiate gravitational waves. Like electromagnetic waves, these should carry energy and momentum and should be identifiable with a suitable detector. For gravitational waves, this would be an object of large mass with a method of detecting any disturbance of it. In 1958 Weber began the design and construction of just such a device. By 1965 he had built a solid aluminum cylinder detector, 3 feet in diameter and weighing 3.5 tons. Bonded around the cylinder were a number of piezoelectric crystals, which generate a voltage when the bar is compressed or extended. Weber claimed that his instruments could detect deformations corresponding to 1 part in 10¹⁶, a difference of about 1/100th the diameter of an atomic nucleus.

Weber was aware of the problems involved in this kind of design. To rule out causes other than gravitational – acoustic, thermal, seismic, etc. – he suspended the cylinder in a vacuum. More significantly he built a second detector 600 miles away from Maryland at the Argonne National Laboratory in Chicago, and only recognized coincident readings as evidence for gravitational waves. He reported the first coincident readings in 1968. He also noted, in 1970, that such readings reached a peak when the cylinders were both oriented in the direction of the galactic center.

Unfortunately, although there were several attempts to replicate Weber's work in the 1970s, none proved successful. Work has, however, continued with more sensitive antennas. Supercooled niobium rods have been installed at the European Laboratory for Particle Physics in Geneva, at Stanford, and at the Louisiana State University for a three-way coincidence experiment. Despite recognizing 60–70 events a day, none have conclusively proved to be coincidental.