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I don't know the exact weight difference between the two setups, but I know you will be adding weight.
I'm assuming that the chrome gumbys are the actual OEM/factory 2008-2010 forged alloys (with aftermarket chroming) that originally came in a polished finish only?
Those are lighter than any aftermarket/replica C6 Z06 rim though the Nittos are most likely a little lighter than the Goodyears that they are replacing.
You will be going lighter actually... Look at the weight difference in the tires alone. I had stock chrome gumbies with Goodyear supercars, bought chrome spiders with toyo t1r and they actually weighed 2-3lbs lighter than stock setup! These runcraps are quite heavy so please don't forget that disadvantage. Plus the chrome gumbies are nowhere near as light as the speedlines they replaced to me.....
The tire weight's are available from a number of sites., Good luck on getting weight of the wheels, it's apparently TOP SECRET info, no manufacturer will commit to the actual weight.
As an example; Bob @ House of Wheels stated that Factory Repro Z06 style wheels were aprx 2 lbs. heavier than stock 5 stars in the same size. Going from Supercar C6 tire sizes to KDW 2's in 265/40 F and 295/35 R and from stock '05 polished wheels to the Fact Repro same size I ended up with the same weight wheel/tire combo as stock.
Heavier wheel + lighter tire = same overall weight.