As the resident Weezerholic on the boards, I shall assist! I've had Precisions, Jazzes, PJ's and now a Gibson G-3. Of all, the jazz nails matt sharp tone. I keep all controls on full, or maybe roll back on the bridge pup a little. Most of Matt's tone came from his ornage matamp head (quite dirty sounding) and (on Pinkerton) he used a green sovtek muff, for things like tired of sex.
As it happens, I'm contemplating a Jazz body with a warmoth neck like Matts. Yeh...I'm sad