In 1974, he received his Ph.D. from Yale University in Engineering and Applied Science under the supervision of Prof. Aris Phillips (Aristoteles Philippidis), with a dissertation titled "The Investigation of Yield Surface by Dislocation Mechanics".
He has also worked on the functional properties of ferroelectric and multiferroic materials, their direct and converse effects, and electrical and thermal conductivity of carbon-nanotube and graphene based nanocomposites.
In recognition of his "outstanding research contributions in theoretical solid mechanics," Weng was awarded William Prager Medal in 2013 by the Society of Engineering Science.
A 3-day, 55-paper symposium on Micromechanics, Composites, and Multifunctional Materials, was held in his honor during the Joint SES 50th Annual Technical Meeting and ASME Applied Mechanics Summer Conference at Brown University.
His professional activities included Editor of Acta Mechanica (1985–2020), Editor-in-Chief, ASME Journal of Engineering Materials and Technology (1992–1997), Chairman of ASME Materials Division (1993–1994), and an international appointee to the University of Hong Kong Visiting Research Professor Scheme (2010–2013).