**First to note, I'm not against any users moving from brand to brand... was eyeing on some Sony mirrorless till recently.
But not sure if I'm making any sense here.... The 5d body does weighs quite abit (nearly 1kg)...but the lens at times are as heavy or even heavier than the body itself (those 2.8 zooms, each weighing about 1-1.5kg).
If you are moving over to Mirrorless to shave some size/weight but pair up with the huge 2.8 zooms (in my memories, the Sony 24-70 and 70-200 are about big as Canon), I seriously doubt you can reduce much weight. Personally, 2kg in the bag vs 1.5kg in the bag, not much diff to me.