He, John Franklin Enders and Frederick Chapman Robbins were awarded a Nobel Prize in Physiology or Medicine in 1954 for showing how to cultivate poliomyelitis viruses in a test tube, using a combination of human embryonic skin and muscle tissue.

In 1936, Weller entered Harvard Medical School, and in 1939 began working under John Franklin Enders, with whom he would later (along with Frederick Chapman Robbins) share the Nobel Prize.

After the War, he returned to Children's Hospital in Boston, and it was there in 1947, that he rejoined Enders in the newly created Research Division of Infectious Diseases.

In 1954, Weller was awarded the George Ledlie prize in recognition of his research on rubella, polio and cytomegalovirus(CMV) viruses.

In addition to his research on polio, for which he won the Nobel Prize, Weller also contributed to treating schistosomiasis, and Coxsackie viruses.