In 1967, Weiss and Marvin Zelen shared the Washington Academy of Sciences award for their contributions in Mathematics. Established in 1939, this award recognizes noteworthy accomplishments by young scientists (40 years of age and under). In May 2010, the NIH held a symposium entitled "Random Walks in Biology and Beyond", in honor of Weiss's 80th birthday and recent retirement. In July 2010, at the Mexican Meeting on Mathematical and Experimental Physics, Weiss was awarded the Leopoldo García-Colín-Scherer Medal. This medal has been established in 2001 and awarded every three years to recognize outstanding international scientists for their contributions to the development of science.
