I owned a Ruger Red Label 3" 20 in the very early 1980s, and found the EXACT same thing with regard to patterns with 3" ammunition, along with a special added bonus of the gun not shooting to where I aimed it. Did I mention I got rid of it?

Hell, if you keep looking about, you can find 6lb 12s (my Darne R10 with sling is just a bit over 6lbs) and with light loads, these are especially sweet guns for extended carry. I also own an Italian "Companion" folding single shot hammerless 12 gauge that is about 5 lbs-it has a 3" chamber, but, coward that I am, I've never touched one off in it. I prefer my retinas attached. I use it as my snowshoe grouse hunting gun, with 30" tube it is a bit like a highwire artists balance pole, and the shots on grouse are out there a ways in winter.

Never underestimate how much of a friend a 7 1/2-8lb lb 12 is when you have 100 rounds of clay birds to shoot at trap league, however. The "one gun" religion often fails to mention the "one type" of shooting they participate, and, expect success in.
Best,
Ted