Here's a couple slices of riff-roarin' rawk from a couple bands that I've already featured on here. Chicago (Fig Dish) meets southern California (Everready). Both of these aggregations were pop-friendly punks from the mid-90s. Fig Dish's "Eyesore" appeared on their "Quiet Storm King" promo cd ep, but this might be a different version (click the hyperlink above for their first, and very scarce single). As for Everready's "Weezer," I don't think it's about the band it's title entails, at least that's my take from the lyrics. Not exactly sure when this single came out - probably 1995/96.
Fig Dish - Eyesore
Everready - Weezer