This song is about going insane in public. Here's some lyric analysis:
"If you want to destroy my sweater, hold this thread as I walk away" - Keep doing what you're doing as I drift further into insanity.
"Watch me unravel, I'll soon be naked" - Watch me drift into insanity, I'll soon be there, naked being full insanity.
"Lying on the floor, I've come undone" - Lying on the floor, I've become mentally Undone.
The opening dialogue is used to show how he is at a party, losing it, and no one notices or cares. The two verses are used to show how he's barely able to think and talk straight on his decent. The part about "I don't want to destroy your tanktop" is showing how other people are on the brink of insanity already, but he's not "pushing them off" like they are to him, then "To see you lying there in your Superman skivvies" shows how every one is on the brink of insanity to begin with, even more so then he was in his "sweater." The music helps illustrate the ever-maddening mind of the guy, as it starts out normal, then at the end is hard, dark, and mad sounding, showing his slow decent into madness. (thanks, Derek - Pittsburgh, PA, for above 2)
Many of the promotional singles sent to radio stations contained an edit that cut the guitar solo short. This was a distribution error, but didn't have much effect because most radio stations played the album version. (thanks, Bertrand - Paris, France)
This was the first Weezer song that Rivers Cuomo ever wrote, back in 1991. Three years later it was released as the band's first single.
Cuomo told Rolling Stone: "I was trying to write a Velvet Underground-type song because I was super into them, and I came up with that guitar riff. I just picked up that acoustic guitar and the first thing I played was that riff. And it just feels so classic to me, even now when the band starts to play it, it just takes over the energy in the room and you're just transported into the world of Weezer. It wasn't until years after I wrote it that I realized it's almost a complete rip-off of 'Sanitarium' by Metallica. It just perfectly encapsulates Weezer to me - you're trying to be cool like Velvet Underground but your metal roots just pump through unconsciously."
Cuomo told Billboard magazine: "It's been the case since our first album that people thought we were just being sarcastic and ironic. When I wrote 'The Sweater Song,' to me it was a very sad song about depression, and people heard it on the radio and thought it was hysterical."