His research has focussed on retroviruses, initially as a means of understanding T-cell leukemia and other cancers, which may be caused by retroviruses. A break-through discovery in 1971 was that the retroviral genome in chickens follows the rules of Mendelian inheritance. Later his work moved on to Human Immunodeficiency Virus, also a retrovirus, and made several new important discoveries, most notably identifying CD4 on lymphocytes as the binding receptor for Human Immunodeficiency Virus. Before becoming professor at University College London, Weiss was Director at The Institute of Cancer, London, from 1980 until 1989, after which he continued as Director of for a further nine years.
Until 2005, Weiss was Editor-in-Chief of the British Journal of Cancer.
His successor, A. L. Harris, states that Weiss showed "clear vision in developing the British Journal of Cancer into multidisciplinary journal with a focus on research that aims to deliver benefits to cancer patients.".