Well, if it's not the sight, and if you're not canting the bow, then I agree - it has to be the tune.

Here's what I'd do. Set your sight so you're hitting dead center in your aim point at 15 yards. Then shoot a couple at 40 and see where the arrow hits. If your arrows group off to the side, then adjust your centershot to bring the point of contact to center.

Then go back to 15 and adjust the sight to hit dead center again. Then go back to 40 and repeat the process there.

After a few repetitions, you'll have the arrow shooting center at all distances. That's a variation of what's called 'walkback tuning.'