Featuring the jazz standard "Birdland", the album is one of the best-sellers in the Columbia jazz catalog. This opening track was a significant commercial success, something not typical of instrumental music. The melody had been performed live by the band as part of "Dr Honoris Causa", which was from Joe Zawinul's eponymous solo album.
Although not mentioned as a live recording in the liner notes, "Rumba Mamá" (a percussion and vocals feature for Manolo Badrena and Alex Acuña) was recorded at the band's concert in Montreux in summer 1976, of which a film would be released on DVD in 2007.
Dan Oppenheimer in a June 1977 review for Rolling Stone felt the band had moved from their earlier music, losing a lot of the space, melodies and airy feel that marked them out from other jazz rock bands, but gaining a new bassist who "has been instrumental in developing their busier, talkative style", and that while their music previously "went up and up only; becoming more ethereal as it went; the new bottom makes all the difference in the world".
Richard Ginell commented in a retrospective review for Allmusic that it was released "just as the jazz-rock movement began to run out of steam", however he felt that "this landmark album proved that there was plenty of creative life left in the idiom."
In February 2011, Heavy Weather was inducted in the Grammy Hall of Fame.