In my experience, if it's <9lbs I can almost always make it sound and play great. Especially P's and 4-bolt J's. Fender necks are easy to adjust, and grey bottom are imho the best pickups Fender ever produced.
Mine is 9.5 lbs, and I don't think it sounds too good. I manage to set it up OK, and sound OK. I think it's the only bass I would not regret selling, and I've had it since I was a kid.
My cousin invested in a '68 P a while back, all original. Very worn, but not beat up. Pickups measure and look the same, but the '68 is much louder. It was a super light specimen, very balanced across the board, no serious dead spots, just super playing and sounding.
I should never played that bass, it made mine feel even worse. I'm amazed these two came out of the same factory with only six years between them.