For the J type tone, the Sadowsky NYC's are typically around 8 pounds or so, and combined with the slightly downsized bodies, they are REALLY comfortable. If you order the lower priced Metro model directly from Roger, you can probably spec one on the lighter side (under 9 pounds). However, the NYC models are routed out for very light weight, and you could probably spec one close to 7 pounds.
In the more modern tone area, the Skjold basses are quite lighweight, and Pete has a model (Lion's Pride) that has a more traditional Fenderish look that he is producing now. Since he is a pure custom shop, you can spec and under 8 pound instrument.
The build time for both the NYC and Skjold is around 8 months or so from order.
Carey Nordstrand is building 'Nordy' models now that are J Bass designs. You could also spec a lightweight version that would be close to the Sadowsky NYC weight. Build time is around 4 months for those, and the price is very good for a boutique instrument.
The Rob Allens are REALLY lightweight, but are specialty instruments meant to sound very organic and acoustic.