I was surfing through and just happened to read this thread.
I own the Browning 81 lightweight stainless BLR in .300 WSM with the straight stock. This rifle along with my Marlin 45/70 are my all time favorites.
Because it is a light rifle you have to make sure you use two hands when shooting, even prone, or the scope will ding your head. My accuracy seems slightly less than a quality bolt action, but not enough to worry about in the field. I made a very long one shot kill on a deer this year, prone supported on my backpack. I forget to hold the forearm and dinged my head, again.
I use the Leupold base and rings. I had Weaver and my scope kept moving probably because it is a magnum. On another deer I shot the concussion from therifle blastcracked my windshield. I was standing beside my truck with the side window openand my rifle was in the bed. I jumped out, grabbed the rifle, worked the lever to chamber a round, and fired.
This rifle is a blast, but never forget you are shooting a magnum in a lightweight. MV out!
EDIT- I found this:
Browning BLR 81 in 300 WSM The stainless are cool though.