My daughter's Senior Pictures.

I'd recommend the Sony NEX-7, yes, you'll be able to blow photos up to 16x20 without any issue, it has a large sensor, high resolution, and good image quality at high ISO.  Its also pretty compact!

The Nikon D800 is a serious professional camera, I think you'll spend a lot on it and not get much value.  

One reason to consider a DSLR, like say the Nikon D5100, is that you'll get a larger lens selection than with the Sony NEX-7, and often having the right lens can make a big difference for photos.  If you got a prime lens with a D5100 such as the 50mm f/1.8 (in addition to the lens that comes with it), that would be great for portraits.

If you have to ask, you're not ready for a big DSLR. Where DSLRs really benefit is their speed and ruggedness. The Sony NEX-7 (or any good mirrorless camera) will not only give you the flexibility you want for great portraits, but even afterwards will make a great camera to travel around with and use in your everyday life. The native 24mp files are big enough to print up to about 18" without ANY resizing at all, which means it will do 20" without a problem. With good shot discipline you could print many many feet. I have a 52" print in a gallery right now that was taken with only 12mp.

Funny the weight of the D800 put you off, because it is actually substantially smaller and lighter than even its own predecessor.

If you are interested in a DSLR, start with something with a lower MP count. The more MPs, the higher quality your lenses need to be to use them, AND that much resolution is going to show imperfections in both your technique and equipment MUCH more than something more modest.