While every component of a bass impacts the tone somewhat, the impact of weight is IMO and IME greatly overstated. IMO, there is NO reason to make an instrument that weighs over 10 pounds... zero reason.
I've played Tommy Kennedy's Fodera a couple of times, and it is stupid lightweight (swamp ash body, reduced Emperor II body size). I've had a chance to A/B it with a couple of my buddies 'boat anchor' 11 and 12 pound Fodera's. Even with Tommy's bass having the neck pickup moved toward the bridge, guess what.... they all sounded very, very, very close
Again, Tommy's 8 pound or so bass balances exactly the same as my old 11 pound Emperor