>D600 2,000 + 16-35 lens---3,359.00 >D7100 1,200 + 16-85 629.99—1,829 >A difference of 1,530 with my selections.
Not sure why are you comparing these two combos.
FX consumer zoom similar to the 16-85 3.5-5.6G is not the 16-35 f/4G VR (that's a quite unique wide-angle zoom, roughly equivalent to 12-24 f/4 DX on DX, but better, cheaper and with VR), but the 24-85 3.5-4.5G and the cost is cheaper than the cost of the 16-85 DX.
In fact as the D7100 has much higher pixel density than the D600 you need much better glass to fully utilise the resolution. The D600 works fine with cheap lenses from film-era.
Yes, there is $800 difference between the bodies, but you get much better camera for that money. If you have $800 there is no reason why to prefer DX.