OK just took the PSU out (Lian-Li 140mm fan still in) of my 6788 and poped it on the scales
approx 5.5kg
ps I know you're PSU is not that bad, what I was sugesting is that you should be able to get away with a 400w psu and even a good one should be lighter than you're current 700w psu
And that you could get a real el-cheapo job which would probably only mass 1kg, it would save weight, but the risk would be too high.
Just poped my enermax pro82+ 525w on the bathroom scales, approx 2kg
You probably don't want to remove your psu to weigh it, same reason I'll not give you a weight for my gameXstreme 700w