Hello Anil.
I have the D7000 and a variety of different lenses that suit my tastes. It is difficult for anyone to say get x, y or z lens as it may not suit your needs or your budget.
Amongst the best zoom lenses you can get for your D7000 are the 70-200 2.8; 24-70 2.8 and 17-55 2.8. All are fast, sharp and generally fantastic but they are big, heavy and expensive! Based on what you've said so far, I don't think these meet your needs as you indicated you didn't want to "lug around heavy lenses". So right off the bat - as is usually the case with lens choices - we are starting down the road of compromise.
If you want a super-light weight zoom then the 55-200VR is excellent however I prefer the 70-300VR which has longer reach but is a bit bigger and heavier. The 55-300VR is also a nice consumer lens but I still prefer the 70-300VR for build and to my eye, image quality (not all agree on this point).
You mention that you don't see the need for focal length overlap - why? Some overlap is a good thing as you won't have to change lenses as often. The 18-105VR (which I have) is quite an amazing lens in it's own right - sharp, great range, light weight but not poorly built either. You really would be hard pressed to find a better bang for your buck lens. However I did upgrade to the 17-55 2.8 but made the trade off between weight, size, range, speed and image quality - and for me it was well worth it!
Have you considered just shooting with primes? I suggest this as primes (as opposed to zooms) are smaller, lighter and generally have better image quality (not always). In your case how about getting say the 35 1.8 and 85 1.8? (I don't like the 50mm focal length as I find it a tad too long for indoors and too short for outdoors - frankly that is the one I'd sell - not the 18-105VR). If you're somewhat interested in this path but don't know if it's for you - try setting your 18-105 at 35mm and/or 85mm and see how you like working at these FLs Primes challenge you not to be lazy with your composition and "zoom" with your feet so to speak. I do have both of these lenses and highly recommend them!
The 18-200 you asked about is a highly polarizing lens. People have wildly differing views on the usefulness of this particular lens. Basically if you really hate changing lenses (although why buy a DSLR if you do?) then the 18-200 is the ultimate one lens solution. It would make most sense as a travel lens where you might not have the time or inclination to swap out lenses. However, the 18-200 - factually speaking - does not have the image quality (the degree of which varies along the range) of even the 18-105VR. The extent to which this bothers you will depend on how picky you are about softness in the corners and in general. Not terrible but certainly noticeable. For these reasons I passed on this lens as I would much prefer say the 18-105 and the 70-300.
I have the Sigma 10-20 - it's a fun lens but I don't use it very much as I find 17mm wide enough for me in the vast majority of cases - however true wide angle shooters would find 17mm woefully inadequate.
Again, these are just my thoughts which are framed around my photography needs.
Decisions, decisions....best of luck with yours and enjoy your camera!