Lightweight flywheel in my opinion is worthy add-on especially if you are already doing the clutch.
Rotating mass takes energy to spin it from one RPM to another. Therefore, it takes power from the engine that could otherwise be used to accelerate the vehicle.
The significant measure of rotating mass is called the mass moment of inertia. To keep it simple, weight is bad, but weight farther from the center-of-rotation is much worse. The mass moment of inertia is measured by the mass (weight) multiplied by the distance between the weight and center of rotation squared. For instance if you had a weight of 10 pounds mass, 5 inches from the center of rotation, its' mass moment of inertia would be 10 lb x 5 in x 5 in = 250 lb in^2. That same 10 pounds only one inch from the center of rotation would only have a mass moment of inertia of 10 lb in^2 (96% less). This is why lower diameter flywheels are an issue and heavy larger wheels can have an effect.
When you were a child you may remember playing on hand pushed marry-go-rounds. Kids would stand on them and other children push to get them spinning. You may also remember that it was much harder to push when there were more kids on the marry-go-round and they stood near the edges.
Now for the stock flywheel. I am told the stock flywheel has a mass moment of inertia of 310 lb in^2 and I used this value in these calculations. Let me warn, the effect of rotating mass is not constant for RPM or road speed. In other words, the effect in 1st gear is different than second, and in any gear the effect changes with speed. This is why, if anybody quotes a given horsepower savings measured on a dyno, it is not accurate because chassis dynos DO NOT simulate accurate transients. They measure horsepower at the wheels just fine, but they can not measure the effect of a lightened flywheel, tires, or wheels. They will measure a difference, it just isn't accurate. But it is easy to calculate the difference.
From simple calculations the stock flywheel (280 lb in^2) takes 10-20 HP to spin it while accelerating in 1st gear. In second gear it takes about 5 HP. In 3rd gear it takes 2-3 HP. Therefore, if your lightweight flywheel had half the stock flywheel mass moment of inertia, you could save half the above values. To me, this would be more significant in a 1/4 mile run where the launch and 1st gear is very important. On a road course, not as important.
You might wonder why 1st gear is so much larger? The engine spins from idle to 6500 RPM in less than 3 seconds in 1st gear. It takes a lot of power to spin this mass to high RPM very quickly. In 4th gear, the flywheel takes 10-20 seconds to go from 4500 to 6500 RPM, therefore, much less power required.