I usually carry on around 60+ lbs of stuff. I get some funny looks going through the airport but it's always worked. I've flown with Alaska Airlines and never had a problem. I just make sure my bacjpack (large Kifaru AMR2) is close to the dimensions of the carryon so it fits in the overhead bin. A couple times it barely fit but sometimes I'm on older planes that have more than enough room in the overhead. I also bring on a giant camera bag that fits under my seat (or also in the overhead) with all my camera gear, etc). It's nice knowing my binos, cameras, spotter etc are with me and will make it! I've never had a problem with security. Just make sure you put your ammunition in a different bag than your rifle and don't carry on any knives, shells, etc.
Sometimes they even offer at the boarding window for people with large items to check them all the way through to my destination for free...but I usually want to carry them on so I make sure everything gets there ok. Alaska Air may be more leaninet than some of the other airlines?
In regard to my rifle and rifle case. Tell the person at the check in that you have a weapon. They'll have you sign a deal that you place in your rifle case that your weapon is unloaded, etc. Once checked in they will have someone escort you to an x-ray machine and check in your rifle. Make sure you have locks for your rifle case or they will likely make you buy them from them!
I gut the foam in my rifle case and replace it with clothes, trekking poles, flyrods, etc until it reaches 50 lb limit. My rifle case is on rollers. This makes it easier getting in and out of airports, etc. I often load other stuff on top of my rifle case on rollers to tote around.