a mirrorless FF camera with a 70-200 2.8 hanging from it will be heavy.
the mirror/prism inside a DSLR is pretty light...
Around a decade ago or so ago, when the micro 4/3 format was introduced more or less in conjunction with the mirrorless interchangeable lens camera idea, A commonly counted benefit was "smaller and lighter", but this does not really hold true, in lenses, in the case of anything much longer than around 100 mm or so. The Early and original idea of saving weight and size no longer holds much water, now that the leading manufacturers of Mirrorless interchangeable lens cameras have introduced full frame size sensor cameras in the case of Panasonic, Sony, Canon, and Nikon. The Sony A7 series cameras are now commonly held to be the most advanced, but this year Canon and Nikon have made tremendous strides, and Panasonic entered the full frame market a few months ago with two models of full frame mirrorless cameras. About a month ago I happened to see the new Panasonic 24 megapixel full frame model with a nice zoom lens sitting on the counter of a Portland,Oregon store. The camera was the personal property one of the clerks who worked there, and he allowed me to handle and examine the camera. Let me put it this way: this was no small camera, and the weight and size were substantial in both the body and the lens. I would say that it would be easily possible to purchase a smaller and lighter single lens reflex which would weigh less than this full frame Panasonic mirrorless.
As far as lenses go, a decade ago there were very few "big glass" options available fot MILC cameras. Today? A relatively good number of lenses are now available,and those lenses are about the same size and weight as for traditional single lens reflex cameras.
there are other cameras besides those four I mentioned above, such as the the cameras made by Leica and by Hasselblad, as well as a few mezzo or medium-format digital mirrorless options (fuji g series) which are pretty large cameras and which use relatively large and heavy lenses.
I think we need to consider that mirrorless does not automatically mean "smaller" nor "lighter". it is no longer 2007