After graduating from New Trier High School, Weese enrolled at the Massachusetts Institute of Technology in 1933 to earn a Bachelor in Architecture degree. Weese also took architecture classes at Yale University starting in 1936. Weese studied under Alvar Aalto at MIT, and fraternized with classmates I.M. Pei and Eero Saarinen. As his schooling was at the height of the Great Depression, Weese avoided studying expensive historical revival styles in favor of more-affordable modern styles. In the summer of 1937, Weese toured northern Europe on a bicycle, fostering his appreciation for the modernist movement.