I suspect accuracy differences between the pencil barrel and the Government profile barrel are likely to be more influenced by the individual barrel and ammunition than you can attribute to the barrel weight.
I second taliv in wondering what do you want to do with this carbine? I have a 6920 as I type this, and while it's reliable, I wouldn't classify it's accuracy much better than "good". It's certainly more than acceptable for my uses, as I bought it to turn money into noise and to sit behind the closet door, "just in case." Right now it's topped with an Aimpoint PRO red dot, which I feel compliments the rifle perfectly given its practical useful range.
Oh, accuracy: the best groups I've gotten out of my particular example are right around 2" at 100 yards for 10-shots, using handloaded Hornady 75gr BTHP match bullets. Using the iron sights it came with. Handloaded 55gr FMJ varies from this, from about 2.5" using Hornady bullets to over 3" using, well, just about anybody else's FMJ pills. I haven't benched the rifle with factory ammo since I first got it, but I distinctly recall American Eagle 55gr FMJ being somewhere around mediocre, well over 3" groups.
But I don't spend much time trying to make pretty groups with my carbine. It gets used to bust clays hanging out at 50 and 100 yards, ringing steel out to 200 yards and of course ventilating lots of paper. All done from standing and improvised prone and sitting positions. At 200-yards, even with run of the mill FMJ ammo, a 10" steel plate is getting hit the majority of the time.