Well considering the curb weight of a base C6 Vette is 3200lbs, I'd say the new Vette will come in under 3350lbs. From what I understand, GM was targeting 3000lbs for the curb weight on the new C7. And given the C6 Z06 comes in at a little over 3100lbs and GM already stated they shaved 99 lbs just off the C7 chassis alone, 3000lbs should be a pretty realistic target.
2013 C6 curb weight per model
That's why I said at least I wanted to estimate high to be sure to be correct!