My Sting is my most resonant bass, it's also got the thickest neck. It doesn't neck-dive, but considering how chunky the neck is, I wonder if it's heavier than my other bass necks. For me, if the mass is responsible for it's sustain, it's a worthwhile trade-off.
I weigh necks all the time. I've found that it's the stiffness that's more responsible for tonal variations than mass with a stiff neck having more of the qualities I look for in a neck such as eveness of response, fullness of tone, and sustain. A stiff neck may not be heavy and a heavy neck may not be stiff.
The steel stiffening rods of Warmoth necks add stiffness and mass. Graphite adds not as much of either, but the best for me is a light stiff all wood neck with a single action trussrod.
I also find shortscale necks are generally stiffer than long scale necks by virtue of their reduced length cantilevered from the body.
