No. A smaller body that weighs less is an advantage.
As is an electronic viewfinder which gives you a better understanding of what your final image will look like.
But because of that they do eat batteries compared to a traditional DSLR. Also if you are carrying pro glass the weight of the body is neither here or there.
I've used some pretty darn heavy camera bodies handheld. In the 35mm real, a Nikon F2 or a Canon F1 with a motor drive certainly is a beast. My F2AS came with an MD2 motor drive, and as it's been loaded pretty much since I bought it I haven't taken the time to remove the motor drive(you can't do it with film in the camera since the power rewind post goes through the baseplate and removing would fog the film) and I think the combo weighs in at 5lbs or so loaded with 10AAs and without a lens. It's almost comical to see it with a pancake lens like the 45mm 2.8 AI-P(smallest lens Nikon has made-a 45mm 2.8GN or 50mm 1.8 Series E will work in a pinch for less money). Granted it's still not as funny looking as my Leitz 50mm collapsible Elmar on my Canon 7.
I've also shot basketball with a 4x5 Speed Graphic, and have trekked around with a Mamiya RB67. I think the Mamiya is the heaviest of all the bunch.
In fact, when I got my Hasselblad back in January, I wanted to carry it everywhere because of how light it was compared to other MF cameras I've had. To be fair, I think my Pentax 645 is lighter, but it has its quirks that makes it far from my favorite camera to use.
In any case, I say all of that because I find that-within reason-heavier bodies do a better job of damping out vibrations. On the lens front, one of the reasons that many folks find mirror lenses so difficult to use well is because they are so light. This can be true of bodies also. Heck, the mirror in the RB67 Pro-SD is 8cmx8cm, and the sheer weight of the body is enough to dampen it(I wish someone else had run with the Bronica EC/EC-TL design of a split mirror where half goes down and half goes up).
Of course, mirror shock isn't an issue on mirrorless.
One of the biggest barriers I see to the Sony FF system, though, is that the native lens selection just isn't that
