My "everything" gun is a 12g 870 w/28" barrel. I consider it moderately heavy...yet I love it.
My father's SKB XL900 (auto) in 12g is lighter than alot of 20g I've held. But it's fixed full and far too pretty to take anywhere but the range and occasional dove field
My father's Fox B (Savage made it years ago...not a real A.H. Fox) in 12g SxS is a nice balance. But it fits horribly, kicks like a mule and, obviously, I shoot like trash with it.
I have an old beater Remington 11 (A-5 patent) with 30" barrels...that thing is HEAVY...but I love it and would use it alot more if bismuth wasn't so dang expensive!!!
Are my shotguns heavy...yep! Will I get rid of any...nope. Am I looking into a light gun for upland/squirrel/rabbit....possible even in 20g....yep! But I'm young. Strong on the muscle, weak in the wallet.