Weston Vernon Jr., 72, who started a lengthy law career in WashingtoN, died of cancer Saturday at his home in Remsenburg, L.I., N.Y.

Born in Logan, Utah, he graduated from Utah State College in 1925, when he came to Washington.

He then earned a law degree from George Washington University and was admitted to the D.C. Bar in 1928.

Mr. Vernon worked with the former law firm of Dunnington, Walker and Gregg here until moving to New York City in the early 1930s, when he became associated with the law firm of Davis, Polk, Wardell, Gardiner and Reed.

A specialist in tax law, he joined the law firm of Milbank, Tweed, Hadley and McCoy and became a partner. Although he was semiretired, he remained with the firm until his death. He had spent much time at the firm's Washington offices.

Mr. Vernon was a past president of the New York State Bar Association and active in the American Bar Association where he was a former chairman of the tax section and later, until his death, chairman of its section on science and technology.

He is survived by his wife, Lillian Malley Vernon, of the home, and three sons, Weston III, of Silver Spring, Robert, of Salt Lake City, and William, of Rocky Mount, Va.

The family suggests that expressions of sympathy may be in the form of contributions to the Cancer Research Institute.