Educated at the Belfast Royal Academy and Clare College, Cambridge, he held positions at the universities of California, Chicago, Harvard and Yale, ultimately holding professorships at Heriot-Watt, and University College Dublin before becoming, in 1984, Erasmus Smith's Professor of Natural and Experimental Philosophy at Trinity College.
Together with his graduate student Robert Phelan, Weaire came up with a counter-example to Lord Kelvin's conjecture on which surface was the most economical way to divide space into cells of equal size with the least surface area. This counter-example is now referred to as the Weaire–Phelan structure. This structure was an integral part of the design of the aquatic centre used in the 2008 Olympics in Beijing.
Weaire has a strong interest in the history of science and has edited several collections of historical essays on Irish physicists.
Relationship to Ira Einhorn
During the convicted murderer Ira Einhorn's time in Ireland, Weaire was his landlord. When Weaire found out about the accusations of murder that Einhorn faced in the U.S., he reported him to the FBI and evicted him. Weaire, and his relationship to Einhorn, was the subject of the 2004 TV show Interpol Investigates (episode entitled Fatal Compulsion). The part of 'Professor Dennis Weaire' was played by actor Robert Randolph Caton. He was previously depicted in the made-for-TV film The Hunt for the Unicorn Killer, which featured Naomi Watts as Holly Maddux, Kevin Anderson as Einhorn, and Ian D. Clark as Weaire.