Interestingly, the Nikon Nikkor VR 70-300mm 1:4,5-5,6 for Nikon 1 weighs 550g while the m.Zuiko 75-300 4.8-6.3 weighs just 423g. This has nothing to do with the sensor size of the systems
perhaps
but with the fact that the Nikkor is more rugged.
If there is any effect of build quality on weight, it will be of only secondary importance in this case.
The main reason for the weight difference between the two lenses is the difference in maximum aperture.
The m.Zuiko's maximum aperture at 300mm is f/6.3, which is 47.6mm.
This gives the entrance pupil a cross-sectional area of (47.6 / 2)^2 x pi = 1781 sq. mm
The Nikkor's maximum aperture at 300mm is f/5.6, which is 53.6mm.
This gives the entrance pupil a cross-sectional area of (53,6 / 2)^2 x pi = 2254 sq. mm
If the weight of lens elements is proportional to their cross-sectional area (which would be the case if they had the same average thickness) then we would expect the Nikkor's elements to weigh 2254/1781 = 1.3 times the m.Zuikos.
And we see the Nikkor weighs 550/423 = 1.3 times as much as the m.Zuiko.
So the difference in weight is explained by the difference in max aperture.