Robert Weir was born to Robert and Mary Katherine Brinckley (or Brinkley) Weir on June 18, 1803 in New York City. His father worked at mercantile and shipping jobs. His mother Mary is remembered for composing the song “The Lord of the Castle.” Robert never graduated from college, and he left a job as a mercantile clerk to pursue painting in 1821 at age 18. He studied art in New York City from 1822 to 1824, teaching himself drawing and painting before departing to study in Italy in 1824. He remained in Florence from 1824 to 1825, then in Rome from 1825 to 1827, during which time he studied the works of Michelangelo, Raphael, and other Italian masters of the Renaissance. He returned to New York in 1827 to care for a sick friend and remained there until 1834, becoming an integral part of its artistic community. He was appointed as Teacher of Drawing (1834–1846) then Professor of Drawing (1846–1876) at the United States Military Academy at West Point, New York.

Weir was considered part of the Hudson River school of American art. One of his best known paintings is The Embarkation of the Pilgrims which hangs in the United States Capitol Rotunda. He was commissioned by the United States Congress in 1837 and the painting was placed in the rotunda in December 1843. His canvases deal principally with historical subjects, though he also did several portraits.

Weir was married twice and had 16 children. Son John Ferguson Weir (born 1841) was a painter and sculptor who became a Member of the National Academy of Design in 1866, and was made director of the Yale University Art School in 1868. Son Julian Alden Weir (born 1852) studied under his father and under J.-L. Gérôme and became a distinguished portrait, figure, and landscape painter. He was one of the founders of the Society of American Artists in 1877, and he became a member of the National Academy of Design (1886) and of the Ten American Painters, New York. Daughter Emma Weir married Thomas Lincoln Casey Sr., an American army officer and Chief of Engineers. Daughter Helen Rutgers Weir married Thomas Sturgis, a developer of Cheyenne, Wyoming, and the second New York City Fire Commissioner.

Weir was the fifth artist to hold the position of art instructor at the academy. During his 42 years (1834–1876) in this post, he instructed many of the future commanders of the American Civil War. Among his notable students at West Point were James Abbott McNeill Whistler and Seth Eastman. He also developed a special relationship with Ulysses S. Grant. He died in New York City on May 1, 1889.