It is often said that archery is a game of little things. More so, I believe it is a game of repeating those little things. Shooting a bow — or at least shooting it well — isn't as easy as it may appear, largely because so many things must be repeated exactly the same way from shot to shot to be consistent. One of those things is centering the sight inside your peep. There are two main factors that influence how well you are able to do this. First, peep size is very important in being able to consistently center up. Second, the number of aiming pins in your sight housing will help determine whether to center the pin itself or the entire housing.
I believe the most critical aspect to this topic is choosing the right peep size. In my experience, the best bet is to find the peep size that appears just slightly larger than your sight housing at full draw. This way, you can center the entire housing by lining the two up with each other. If you can see any space between your peep and your sight housing, you know you aren't centered. Even a peep opening that's a little larger is OK, especially for hunting, because it lets in more light. What you never want is a peep sight that appears smaller than the sight housing at full draw. This makes it almost impossible to consistently center the sight, while also obstructing your view of the sight's bubble level and restricting the amount of light that is able to pass through the peep to your eye — diminishing the detail with which you are able to see your target and reducing your ability to shoot in low-light situations. Another thing you may find helpful is to add a fluorescent color ring around your sight housing to make it more visible and easier to center.
Next, you have to decide whether to center the entire housing or the individual pins. If you're shooting a single-pin sight, obviously you will center both. With multi-pin sights, you can only center one pin at a time. So, I feel it is easier to just center the entire housing. However, if you feel more comfortable centering the pin, that's fine as long as you do it every shot. If you center your pin one shot, then the housing the next, it will drastically change the point of impact. I believe one of the main reasons archers struggle to shoot consistently is because they don't anchor consistently in relation to their sight/pins. That's why I believe centering the entire housing inside the peep on every shot is the best method, because it maintains a consistent anchor point regardless of the pin actually being used for aiming.
As I said at the outset, shooting a bow consistently is not as easy as it may appear. It's a game made up of hundreds of tiny things that all affect the accuracy of the shot. Archery is all about repeatability. If you're still doing the old "paper plate" test to determine whether you're field ready, then this article probably isn't for you. But if you want to live up to your full potential, try fine-tuning your sight picture to make it easier to center your sight housing in your peep. Pick a peep size that is just slightly larger than your sight housing at full draw. Then decide whether to center your pins or your housing and commit to your choice — there's no way to do both consistently! I know this seems relatively simple, but it is vital when it comes to accuracy, and it will make you a better shot.