In 1967, he joined the faculty of the Hebrew University of Jerusalem; and since 1990 occupied the Miriam and Julius Vinik Chair in Mathematics (Emeritus since 2009).

Weiss held visiting positions at Stanford, MSRI, and IBM Research Center.

One of Weiss's students is Elon Lindenstrauss, a 2010 recipient of the Fields Medal.

Weiss gave an invited address at the International Congress of Mathematicians 1974, was twice the main speaker at a Conference Board of Mathematical Sciences (1979 and 1995), gave the M.B.Porter Distinguished Lecture Series at Rice University (1998).

In 2000 Weiss was elected as a Foreign Honorary Member of the American Academy of Arts and Sciences.