The distance the snow is thrown is directly related to the speed of the snow particles when they come off of the impeller, whether the impeller is heavy or lightwweight, and that speed should be the same as the impeller speed at the moment the snow separates from the impeller. A heavy impeller won't run at a faster rpm and would work the engine harder than a lightweight impeller. If you had 2 identical snowblowers - one with a heavy impeller installed, and the other with the light impeller, I think the governor would control the engine speed to the same rpm regardless of which impeller is installed, consequently, given the same snowblowers, and throwing the same snow, but with 2 different weight impellers, won't change the throwing distance. One engine will work harder than the other in the process, however.

If you install an impeller kit, you lengthen the impeller radius by the length of the rubber sticking out beyond the edge of the original impeller, and consequently that add'l impeller radius results in add'l speed at the outer edge of the impeller given the same impeller rpm, so the snow flies further.

Another way to look at this question is to compare snow throwing distance to how far a golf ball can be hit. Most drivers have the same coefficient of restitution, so consequently, the statistic everybody talks about, related to how far the ball can be hit, is club head speed. No one in the golfing world ever talks about the weight of the club a golfer uses as an indication of how far the ball is hit. The weight of the club, however, affects how fast you can swing the club, and consequently, how fast the club head speed is. I've never heard anyone say that if there are 2 golfers who have the same club head speed, that one of them can hit the ball further than the other because his driver is heavier.

Time for a good stiff drink.