Looking at cameras again and am heavily leaning towards the Sony A6500 for climbing photography. Currently bringing a Canon EOS 5D MK II with me, which I really like the camera and think it takes high enough resolution photos and environmental sealing. But the thing is fairly heavy and bulky for mountaineering purposes. The A6500 has a higher MP sensor (24 vs. 21), is nearly a full pound lighter (400g lighter), has image stabilization (the EOS 5D MK II does not!), and is just a much smaller camera. Downsides are worse low level light capability and a battery which doesn't last as long. I get that lenses and such also add a bunch of weight, but in reality I'm climbing with a 50mm lens and maaaaaybe a 24-70. So.
I'm impressed that you drag a 5d MK II up mountains. I have my own, much less expensive DSLR, and I barely take it anywhere these days. I think you'll enjoy the mirrorless camera much more. I'm convinced they're the future of prosumer grade photography.