WASHINGTON, DC.-Museum administrator and legal arts expert Stephen Edward Weil, 77, died. He studied law at Brown University and then received an L.L.B. from Columbia University Law School in 1956. From 1963 to 1967 he was a vice president and general manager of the Marlborough Gallery. He was also an administrator, secretary and trustee of the Whitney in New York from then until 1974. In 1974 he became the deputy director of the Smithsonian's Hirshhorn Museum and Sculpture Garden.