William Weir studied medicine at the University of Glasgow and became a licentiate of the Faculty of Physicians and Surgeons of Glasgow in 1814, going on to become a Fellow in 1816. He graduated MD from the University of Glasgow in 1829.

He worked at the Glasgow Royal Infirmary initially as a surgeon, before becoming Physician to the Infirmary in 1840. He also worked as Physician to the Barony Parish Fever Hospital in Glasgow.

Weir worked as a lecturer in several of Glasgow's medical schools. He was Lecturer of Clinical Medicine at the Glasgow Royal Infirmary Medical School, Lecturer on the Practice of Medicine at Portland Street Medical School and Lecturer at the Anderson Institute.

Weir was President of the College from 1847 to 1849. ]]>