Justin, you may be thinking the old British "rule of 96": the gun ought to weigh 96X the shot charge. That's not bad thinking, and it'd mean you'd want a gun of around 7 1/2# if you're shooting 1 1/4 oz.
Personally, I think if you're only shooting 1 1/4 oz occasionally, and especially if you're shooting lower velocities--like we've been talking about, as opposed to the 3 3/4 DE (1330 fps) longtime standard American load (not to mention the newer ones, pushing up to 1500 fps)--you're OK with a slightly lighter gun. I have a (modern) Miroku sxs, about 6 3/4, in which I'd use such loads. But with the pheasant limit being no more than 3 everywhere except Kansas, I'd hope that I wouldn't shoot more than about 5 of them a day.
