In my limited experience, it's really hard to find to find a light JB. I had one in Olympic White with a tort pg that had been professionally set up and played wonderfully. I loved it but it weighed just shy of 12 pounds on my calibrated scale. I tried to hang with it but it was just toooo heavy. Sold it and bought a 9-lb MIM, which I will sell as soon as I find a 7-lb JB.
I think it's asking too much of the jazz body size combined with alder. As much as I like a jazz, there are just too many other great lightweight basses out there. I have a 7-lb PJ that gets most of my Fender playing time (I'm constantly moving back and forth from Gibson to Fender to Hagstrom as the mood strikes me), but I WOULD like to have a jazz bass that's not a boat anchor. Maybe one with a poplar body, I dunno.