Is there an advantage to using heavier shot like 7-1/2 vs. 8 for sporting clays targets at longer distances like 40+ yards? Please explain.
Yes, there is some. With all other variables being equal, the shot pattern of the 7-1/2 shot shell will maintain its integrity over a longer distance than the shell with 8 shot. Using a 7-1/2 shell might also be a good idea on longer distance targets and those targets that are harder to break such as an edge-on standard target and rabbits at longer distances. A battue target, or other target presentation showing a lot of belly or face-area, are a bit easier to break so you might consider switching to a smaller shot size (#8, 8-1/2 or even a 9) depending on the distance.