My Precision is 8 1/2 lbs and neck dives. I purchased a strap from Pinegrove to counter this. The result? A nice bass and a nice strap.
https://www.pinegroveleather.com
I had this problem when switching from a J to a P.
I found it's all in the EQ - I keep the bass and treble at noon, bump the mids at 1k and 1.5k and adjust the tone knob to suit, normally 9/10.