The beginning of Heart Songs starts off very slow, an almost un-weezer sound. Rivers references pre-weezer events and artists, still in this odd sounding tone. Gradually the instrumentals get louder and more distinct, as instruments are added. This takes about the first half of the song, but then suddenly, the electric guitar and orchestral background sounds are added, leading into the full blast of Weezer's trademark sound.
This song represents the band's struggle in finding identity. The first half of the song is simply explaining all the different musical inspirations that shaped Rivers' style. The first half of his life was spent trying to find his musical identity, from Michael Jackson's pop hits to Nirvana's hard shreds. Not surprisingly, the first large shift in instrumentals came "back in 1991" when he discovered Nirvana: "then I heard the chords that broke the chains." The music escalates from there, and leads up to a (proportionally) short climax. This is because Weezer's success seeds from the confused times, when the listener has no idea whether the song will remain acoustic and solemn or become larger and noteworthy.
Whether this is the intention Weezer had in writing it, or if I'm just a crazy fan trying to find meaning in it all, I don't know. But if Rivers intentionally integrated such brilliance into three minutes, the themes of the song alone deserve to be noted, whether you enjoy the song or not.