Ya, many of the "big bore" rifles are heavy, but not all.
There can be a price to pay with recoil, but there are those who seem to not mind that factor or?

My RUGER #1s is not in the class of the heavy weights, listed in the catalog as the "Medium Sporter" at 7 1/4lbs.
Now add a 2X7 scope and mounts and it still won't make the heavy wt. class.
It may not officially make the Big Bore class, but with a 350 - 425gr slug at 2100 - 2200fps the difference will never be known by any North American animal.
Years ago, I had a RUGER #1B in 22/250, that someone had cut down from 26 to 22" and it was one of the handiest rifles I ever used. The #1B is listed at 8 1/4lbs, and I doubt the loss of 4" of barrel would bring it down to the wt. of the #1s - 45/70 - with that barrel which looks a lot like a shotgun tube.
So, This 45/70 with it's 22" barrel is light and handy and a joy to carry in the field and with the big/thick recoil pad I have added Plus the sissy pad filled with #5 shot for bench use, the recoil is being managed quite well.
There is however, a slight difference in recoil

between the long departed 22/250 and this 45/70.
Keep em coming!
CDOC