In my brief experience these past few weeks with the Canon I am finding the size the biggest drawback to the system. It's not a huge issue, and the use of a sling strap helps greatly. But the size and weight of not only the camera but the lenses means I end up carrying more gear. The 24-105L is a great "walk around lens" but I find the 35/1.4 and 85/1.2 don't get left behind very often, as IQ trumps everything else for me, and compared to hauling my wife's shopping it really is no big deal.
I'm going to add a wide to the mix (16-35 or 17-40) for shooting at Angkor Wat this week, so tomorrow it's off to the camera shops of Bangkok.
This often happens when photographers buy the biggest lenses, and sometimes too many of them: they complain that the system is too big & heavy. But the Canon system is not necessarily that big & heavy. The Canon 85/1.2 is the biggest and heaviest 85. The Sigma 35/1.4 is even bigger and heavier than the Canon 35/1.4.
Happily, Canon offers some very good small lenses:
24/2.8 IS
28/2.8 IS
35/2 IS
40/2.8 STM pancake
85/1.8
Any of the above will "shrink" the system.
Possible substitutions for smaller size & weight include:
24/1.4L instead of the 16-35/2.8L
24/2.8 IS instead of the 24/1.4L
35/2 IS instead of the 35/1.4L
85/1.8 or 50/1.2L instead of 85/1.2L
135/2L instead of the 70-200/2.8L IS
70-200/4L IS instead of the 70-200/2.8L IS
100/2.8L IS instead of any 70-200
The 5DIII with the 40/2.8 STM pancake feels like a much smaller camera.
The new 35/2 IS and the 85/1.8 would make a great "walkaround" kit.
And the new 24-70/2.8L II, although rather large, is so good that it can substitute for a number lenses. It is smaller & lighter than the original 24-70, and offers better image quality.
Some of the small lenses are older designs and not so good, like the 20/2.8, 28/1.8, the old 28/2.8 and the old 35/2.