Theoretically a F/4 FF zoom would give you a 'better' image since it gets shallower DoF and better high-ISO to compensate for the slower aperture. Tamron 24-70VC and a D800 would be about the same weight as any APS-C deal.
An f/2.8 standard zoom for APS-C or larger sensor is going to be hefty, no matter what. The Canon 17-55 is 22.9oz. The Nikon 17-55 is 26.6oz. The Sigma 17-50 OS is 19.9oz. The Tamron 17-50 would seem to be the lightest at 15.5oz. Still this is practically a pound of glass and not what most people would consider to be a light lens. Plus it lacks Image Stabilization, and it does not have USM/HSM like the Canon and Sigma models. The Nikkor also lacks VR.
35.9 oz (1 kg)
Nikon D3200
sigma 17-50 f/2.8 EX DC OS HSM
JR
This. Or with the Tamron 17-50 f/2.8 VC = 1.025 kg with D3200
