After holding a series of odd jobs, he began painting at the age of 22. His first exhibition consisted mostly of large-format acrylic paintings of imaginary seals and stamps; he would retain the flatness and limited color range of these works, but would move into the depiction of bodies and cartoon characters, the latter of which led him to be grouped with Pop Art as the 1960s progressed.
The spareness of his technique often seems more akin to the school known as Minimalism, however, and indeed his closest personal associations were with artists such as Dan Flavin and Donald Judd, the latter of whom wrote a laudatory essay on Wesley's early work and later set aside a space for him at his complex in Marfa, Texas. Wesley himself considers his work to be aligned with Surrealism, and many of his paintings since the 1960s have taken this dimension yet further, while retaining an extremely limited range of colors and a sign-like flatness.
Several retrospectives of his work have been held, the most recent at the P.S.1 Contemporary Art Center in 2000. He was invited to design the cover for the catalogue of the 2006 Armory Show, and his recent paintings were given a substantial amount of space at the Fredericks and Freiser Gallery booth, which represents him. Replicas of his paintings were also featured in the window of the Hermès boutique on Madison Avenue for the duration of the show.
Until her death in 1996, Wesley was married to the American writer Hannah Green. The playwright and painter Patricia Broderick, who died in 2003, was his partner for the last six years of her life.