Some guys like the "weight" out front, some to the rear, some balanced in the hand, I like a hair of rear bias myself. I did some experimenting recently and I found that if I turned my butt hook the opposite way so it rested on top of my shoulder that it worked fantastic with a slight rear biased weight.
The other two things were that a lightweight rifle moved around more than I like, and that a heavy rifle causes fatigue too quickly.
I haven't weighed it but my AGT Vulcan 2 sits real well with a medium weight scope and a slight rear bias weight. I don't have a butt hook on it but if I pull it in to the shoulder it's a great offhand rifle. A couple weeks ago I got 9/9 on a 2" diamond at 35Y which is about as good I can do considering I don't practice much.
My 10.lb FWB 601 was annoyingly front heavy so when I took that weight off the front it became a whole different and superior rifle in offhand for me??!!
I have a lightweight Steyr LGB1 that is too light for me at 7.9 lbs for offhand, I never have been able to shoot it as well as I had originally thought I'd be able to.
I'm 5'7"/ 165lb/ 60 years old, and so far a 9.5-10lb rifle including scope, etc, reasonably centered weight, or biased to the rear, is the best for my offhand.