I’ve owned a canon 6d for a few years now and shot over a hundred weddings plus various other stuff with it. As I no longer shoot weddings and only use it for personal I’d like to downscale to either a good compact or mirrorless that’s smaller and hS a near equal image quality if that’s possible. Any recommendations?
You might want to have a look at this very similar thread.
https://www.talkphotography.co.uk/threads/mirrorless-what-camera.702969/
To get similar image quality and low light performance etc. in a mirrorless camera you will need to have a look at what is available from the manufacturers that produce full frame mirrorless. Panaonic, Sony, Canon or Nikon.
Panasonic options will be heavier than your 6d.
Sony are the current market leaders in terms of the capability of both their current range of cameras and lens choice, there are several lens options for the system that are small and light weight or if you need the ultimate image quality they can offer lens options for that too, although those lenses won't offer much of a weight saving against dslr equivalents. You also have the option of using your existing Canon lenses with an adaptor like the MC-11.
Canon would allow you to keep your existing lenses and use via their adaptor.
Nikon have probably the best ergonomics of any of the current available full frame mirrorless systems, but limited native lens options at the moment.
All of the current ranges of mirrorless full frame cameras are better cameras than your 6d.
If you are happy enough to drop down to an inferior APSC sensor, Fuji, Nikon, Sony & Canon all have mirrorless APSC options. APSC lenses are generally smaller and lighter so there is a further weight saving to be had here. For APSC Fuji have the best range of lenses.
To get the ultimate light weight set up you could also look at Panasonic and Olympus M43 but you will lose a lot of sensor performance.