I disagree with this statement - if he's saving 9 lbs per wheel, using the widely accepted adage that one pound of unsprung weight is roughly equivalent of eight pounds of sprung weight, that would be the same as removing 288lbs from the interior.
We can throw out some other adages - every 100lbs removed is equal to 100hp, 1" of brake rotor and 1" of tire width...
Increasing wheel diameter will have an exactly negative effect...you're moving the heaviest part of the wheel/tire combo (the bead and related tire-mounting area) farther outward from the center of the spindle. More energy wasted getting it moving and slowing it down. If at all possible run the smallest rims you can. This will offset some of his gain from the weight savings, but certainly not all of it.
Lightweight wheels were one of the modifications I found most beneficial on my cars. Whether you can feel it or not is up to the accuracy of your own butt dyno - whether it improves your lap times is a quantitative and important measure. Weight is the single most important modification variable on a road course - that's why most, if not all classes run in wheel to wheel competition have some type of major limiting weight factor not only power to weight ratio but a weight limit period. Weight makes the car work less hard to turn, accelerate, and decelerate - it makes it more predictable and easier to control doing all three, and it wears your parts down at a much smaller rate than a heavier car. You consume less fuel, less brake, less tire...
Well, the extra rotational inertia of a heavier wheel or tire contributes to the effective linear inertia of the car, just like extra weight in the cabin would, as you said. But, the theoretical absolute upper limit (that I've been given by both MIT and Harvey Mudd engineering geeks) is 1 pound more at the surface of the tire tread contributes to inertia as if it were 2 pounds in the cabin, contrary to the old racer's myth. If you're talking about the wheel itself, the farthest out the weight can be added is the rim, again as you said. So, for an 18" rim with a 25" tire, the "bonus" weight drops from a maximum of 1 pound per pound to about 1/2 pound per pound. The bonus weight is less than that if it's not all concentrated at the lip.
So if you want a realistic estimate of how much weight savings you're going to realize for your money, multiply the weight loss from wheels by about 1.3-1.4. This is based on data that I've been given by true propeller heads and I'm talking about rotational mass (not unsprung weight), which is what is going to effect acceleration and braking, per the original post. I don't disagree, at all, that there are significant benefits in wheel control to be had in lowering unsprung weight...but even that benefit is muted on super smooth surfaces. btw, the only other really credible estimate I've ever seen regarding reduction in rotational mass vs. "cabin weight" is in Herb Adams' book, where he gives a 1:3 ratio, at the axle...which needs to be corrected for rim diameter and distance of total mass from axis, I believe.
For competition use, at the highest levels, it is an advantage and, like you said, you have to do everything you can...We did quite a bit of testing on the Z06, using both oem and CCW wheels (about 4lbs corner) and couldn't find any time that was consistent and repeatable, but that was autocrossing, where we only had 60 seconds per sample, not multiple minutes, like road racing.
btw, the Cobra R, I've been told by those that actually run them scale at 22#, so the weight difference is actually 6#. (edit: oops, that's for the 17X9" iirc)
And, finally, the butt dyno is the most inaccurate form of measurement...at least mine is, maybe some of you guys are more sensitive
So, yeah, you're absolutely right, imho, there's a reason why competitive race teams run the lightest wheels that provide sufficient strength. But, in the "real world", going with superzoomy, super light wheels isn't worth the money...again, imho. If you think about it, in terms of acceleration and braking, the weight of tires is actually more important.