My old Fender J'78 is/was a really heavy beast. With the Badass bridge and three massive brass knobs and three(!) pickups it was somewhere around 8(!) kg...
The tone was fantastic, but I got a slipped disc from that bass. Now it and I have undergone surgery. The bass has a new body from Guitarbuild, a nice very light swamp ash body, not complete, paint job is still to be done. It will look like the original, but without a lot of weight. It will certainly affect the tone, but a bass that won't get played has no tone after all. Still, the neck is a massive chunk of maple, even if it is rather slim. You could club an ox with that. I had another body made for the bass some years ago, but I forgot telling the guy I wanted the 70's position of the bridge pickup. It was a very good looking body, but I never felt at home with the "misplaced" pickup, so that body went to an old defretted 70's Jazz neck. Also a project that is still lying waiting to be completed. Unfortunately my pic's went down the Photobucket drain. I get new pic's in a while...