Brian,
Parker also made 12 gauge guns on #3 frames. I own 12 gauge Parkers on frame sizes 1,2, and 3.
The #1 frame guns weigh 7 to 7.5 lbs.
The #2 frame guns weigh under 8 lbs to almost 9 lbs.
The #3 frame gun weighs 10 lbs.
From the above rather small sample set one could deduce their intended uses. A light gun for long upland hunts with loads that won't loosen every filling in one's mouth. The #2 frames are great all around guns from pheasants to ducks to targets with light to occasional use of heavy loads. Finally, the big old #3 frame at 10 lbs was likely ordered for the duck blind or boat with heavy loads.
The Parker order books list guns by weight not frame size.
Just my not so humble opinion...
Mark