While I agree with Ksanti that the weight of the d600 plus lens is not really that much considering all things. I have no issue taking my DSLR, plus 10-20 + 24-70 + 300mm f4 on long hikes (5000ft, 18 miles).
But there are plenty of times when I want to go light, or not both taking anything at all. Maybe I am just popping into the local wildlife refuge or a friends dinner party, walking to work, etc. I also like to make hard and fast trips in the mountains, normally on skis, and have spent thousands buying the lightest gear around, everything gets weighed and purchased are decided by factoring in weight. E.g. I purchased a nexus phone because it was 12g lighter than an iPhone. I've drilled holes in my ski boots, cut off all the straps from my backpack, etc. in these cases I absolutely do not want a DSLR with me.
I spent years playing with fixed lens P&S but could never really find one I liked the most. In the end I purchased a olympus epm2 m43 camera. Weighs a mere 270g and gives stunning image quality. M43 cameras used to be dogged by underperforming sensors but olympus realized they should just use a Sony-based sensor and now their sensors actually out perform most DSLRs when Normalised (that is the quantum efficiency is higher than almost all other sensors). My epm2 has almost identical performance to my D90, same Dynamic range, same high ISO performance. To put this another way, modern m43 camera equal or outperform the best canon crop sensor money can buy, e.g. they are at least as good as the canon 7D/650D etc.
Like all recent Sony sensors the shadows are very clean giving a very good DR, somewhat comparable to a canon 5dmkII at base ISOs (but without the banding issues of earlier canon sensors).
High ISO performance is clearly a step behind a modern FF camera, expire being more efficient than most DSLR sensors it cannot make up that size difference. However, you also have to figure lenses. Many people with a FF camera will shoot an f/4 lens like the canon 24-105 or Nikon 24-120. You can gain back the high ISO performance crown by using a fats prime on a m43 camera and end up with a system that is still smaller and lighter.
I certainly have no issues producing professional quality images from my little epm2. It haily fits in my jacket pocket, and my ski pants. There is a full line of lenses, with several real beauties. Scene I wanted a system for lightweight use I actually kept mostly to the slower plastic kit lenses, getting a wide to moderate tele in around 100g is insane, as is a 80-300mm equivalent lens in 190g.
Still, I don't think I would ever replace a DSLR with an evil camera. The epm2 supports my DSLR nicely, especially when/if I move to a D800. There are things that no mirror less will ever really compete successfully at, at least not yet.
Viewfinder: my m43 has no viewfinder, which keeps cost and weight down. Composing on the back screen is not nice compared to a proper optical viewfinder, especially a FF viewfinder. Electronic viewfinders are no where near as pleasing as an optical viewfinder with current technology, but I could imagine in 10 years time things are better. Thing is any compact will have the same issue and most Sony DSLRs have gove this way. Composing and stabalising at arms reach without pressing the camera against your head just is no where near as stable.
The static aF is fine but continuous is far behind a DSLR. But Nikon has shown the world how to do things properly, their Nikon 1 AF-C is at least as good as my D90. If Nikon designed a professional serious camera with their hybrid technology they would be onto a winner.
Small size: For big lenses you just plain old need to have a bigger camera to balance and support things. And as soon as you have big lenses the fact the camera is small is kind of irrelevant.
Shallow DoF. Contrary to some like Ksanti would say you can get very nice very shallow DoF images from the m43 camera, there are plenty of fast primes around and if you know what you are doing with the moderate tele primes you can get a DOF comparable to a FF camera. Where the smaller sensor camera just cannot compete is in the wide but fast category, e.g a 24mm f1.4 prime on a FF is impossible to replicate on m43. If you only shoot portraiture and like the wide but shallow look, then m43 is not ideal.
I chose the epm2 mostly because it is the smallest, lightest and cheapest but shares the same sensor, metering and AF system of the 1000£ omd5. Very few physical controls but I shoot 95% of the time in aperture priority mode, so easily set up the real wheel and buttons to control aperture and exposure comp. so lack of controls really has been no issue.