The story
From the band's name Weezer, ultimately from wheezer. The band's name was taken from member Rivers Cuomo's childhood nickname Weezer, which was given by his father in reference to the Our Gang character Wheezer, played by Bobby Hutchins. His character was given the name reportedly due to Hutchins running around so much on his first day at the film studio that he began wheezing.
Etymology from Wiktionary, CC BY-SA 4.0.