Care to put the actual weights down? I can't find any weight info on the ancient 35-105 f2.8 (I'm assuming it's the Tamron)
Anyhow, if you start comparing apples to apples instead of cherry picking lenses, the picture is quite different:
D700: 1075g with battery
D300: 903g with battery
Sigma 12-24 FX: 615g
Sigma 8-16 DX: 555g
Nikon 14-24 FX: 1000g (arguably a closer match to the 11-16 than the 17-35)
Tokina 11-16 DX: 548g
Nikon 24-70 FX: 902g (again a much better comparison both in FL and build quality)
Nikon 17-55 DX: 760g
Totals:
FX body + lenses: 3592g
DX body + lenses: 2766g
Difference: 826g or 1.82lbs, or a 25% difference
Also, the above comparison does not consider bulk, of which the 11-16 and 17-55 are considerably smaller than their FX counterparts.
It is true that once you start getting to longer FLs, the differences diminish. That is partly why you don't see Nikon making a 50-135 or 50-150 DX lens- it would probably end up too similar to the 70-200 in size, weight, and cost.