Moving your sight does nothing but change the point of impact. Tuning is the process of making sure that the arrows are being shot out of the bow with optimum flight. Tuning starts with the arrow. Tips need to be in line with the arrow shaft. If inserts are not installed correctly, the broadhead may not be tuned to the shaft. Same can be said if the arrows are not cut correctly.
Next comes tuning the bow. Tuning is a series of adjustments made to get optimal arrow flight. What is tuned is different to many folks. Some consider a bullet hole through paper tuned. Others consider MOA (1"/10 yrds) broadhead groups tuned. Others want broadhead groups and field tip groups to hit at the same point of impact. That I believe is the goal a bowhunter should achieve. I consider tuned to mean that the bow is capable of putting together 4" broadhead groups at 40 and have the field tip and broadheads impact the same place on the target.
Once the bow's string has been broken in (no creep, etc.) the tuning process can get serious. The Easton Tuning Guide is considered one of the best resources for tuning. Basically, tuning consists of making nock set (or D loop) adjustments up or down, and arrow rest adjustments from left to right in small increments to get optimal arrow flight. If your broadheads hit higher or lower than your field tips a nock set adjustment should be made. If your broadheads are hitting left or right of the field tips, a rest adjustment should be made.
Only move your sight to change the impact position of your group once you've gotten the bow tuned by moving the rest and nock set.
Things like improper cam timing, fletching contact, and other things can make tuning a pain, but it is well worth it once you get to that result.
Good Luck,
Nick