If you're only doing it to save some weight on the body and keep using the same lenses...don't bother.
The 6D weighs 755g, the 7Dii 950g. The Sony A7R III weighs 657g, add for example the metabones adapter and you'll end up at 657+143=800g which is actually heavier than the 6D and only 150g lighter than the 7Dii. To me personally I doubt this will make a real noticeable difference as in a physical advantage.
Also the cost of trading up for the 150g weight benefit would probably be more expensive than seeing a medical specialist to look at your situation.(maybe a custom made brace?)
Also personally I doubted the switch a while back, even considered Nikon, but the simple ergonomics of Canon withheld me from doing so. Too much bells and whistles on the other brands including a million buttons and dials on the camera.
Having said that, me and my girlfriend went to a nightphotography workshop at out local camerashop yesterday and a lot of people used Fuji's, Sony's and other small things I can't identify. I was quite impressed with what they achieved. Bottom line, if you adapt to a mirrorless system all together, the combinations will be a lot smaller and lighter than your current gear. And possibly even better.
And it might be painful to hear as a Canon enthousiast, but the competition has done more in the last years to please the customers than Canon is willing to do. So switching to a different platform is (certainly on paper) a wise step to make. But since I'm not the shortest and have quite large hands, the ergonomics and total cost are holding me back from switching.
I hope you find a good solution for your situation.
PS: I do have a small GoPro Session that I take with me on holidays. If the circumstances are too difficult or heavy to take my DSLR or just typically in favor of the GoPro I'm taking that. And I'm quite happy with the video's and photos that it takes.