I had the reliced sunburst one a couple of years ago, if I remember it weighed about 8.5 lbs, no problem with neck dive as far as I remember. Traded it in for my Matt Freeman Squier and didn't notice any huge difference in weight.
IMO, if it plays and sounds nice maybe try to add a little weight in the pickup to pot route under the scratchplate, also maybe a Hi-mass bridge would help. Believe it or not some players seek out light weight P basses, some older Fenders are heavey (10 -12 ibs) but 8 - 9 ibs is about the norm.