The high (static) weight of the GH3 is required to match the high (dynamic) weight (inertia) of an acoustic piano. Last month I had a piano exam and the exam piano was has "heavy" as my GH3, which actually matches my upright piano weight as well.
I think that the only way to get a digital piano with high dynamic inertia and low static weight is to purchase one of the top models from Kawai or Yamaha. Otherwise you risk to purchase a piano which is too light (or in case of the GH3, a piano with the correct "weight" but in a wrong mode).
When purchasing a low/middle cost digital piano always compare it to the acoustic pianos in the shop: when I did it only the GH3 was as "heavy" as acoustic pianos, all the other (low/middle cost) were lighter.