You need to decide if you want a rifle that is nice to hunt with (light) or nice to shoot at the bench (heavy).
My .375 is 8.25 lbs but it has a good stock design and the length of pull is correct for me, it also has a good quality recoil pad fitted so I have no problem with it even in the prone position.
Talk to your gunsmith and have him (or her) build you a well fitted rifle or alter the current stock. In my opinion you should have a stock that is as long as possible as it will be easier to control recoil (and it prevents you mounting it on your arm as opposed to in your shoulder), you should see 2 to 3 fingers between your thumb and nose this will also help prevent you joining the "half moon club" (not a nice thing on a .375
). The balance is also very important and it should balance near the front main screw as it will make carrying more comfortable and it also helps with the felt recoil.
I feel ideal weights are as follows:
Transitional bore .375 type rifles: 8 to 9 lbs
Medium bore .458 type rifles :9 to 10 lbs
Large bore .500 type rifles : 10 to 11 lbs
The big question is are you going to be able to carry your rifle all day and still be able to shoot it well when your trophy (?) is in your sights ?