I have a tough time shooting most guns that fall under 6lbs well, regardless of gauge.
Single exception is a Remington model 17 pump. It isn't much under 6 lbs, and goes over 6 when the magazine and chamber are in the happy condition. If I had extra common sense, I'd sell EVERYTHING else and become the man with but a single gun.
An ounce in the Remington sure gets my attention. Especially with the 21" barrel installed. I imagine a sub 6 lb 12 would do the same.
I'm less of a zealot on weight, as I become more "seasoned". I don't want the field guns much heavier than 7, and 6 1/2 is preferable, regardless of gauge. I have two near 8 lb pumps I could shoot at the range all day long, but, they almost never go into a woods with me.
The 5 3/4lb Darne 28 is a difficult taskmaster, for me.
Best,
Ted
