Q: Why are the yolks of my chickens' eggs settling to one side?
A: Of course, we can't know for sure what may be going on, but we can offer some information that may assist you in figuring it out!
First of all, it's important to understand what it is that causes egg yolks to stay centered in the first place. The chalazae are the parts of the egg that are sort of like springs, and they act to hold the yolk in place. The chalazae are the think whitish parts you will have seen on either side of the yolk. Sometimes people will choose to remove this part of the egg when cooking, since it is thicker than the rest of the egg, and if you are making a custard or pudding it can sometimes make a difference. But as an egg gets older, the chalaza (singluar - chalaza; plural - chalazae) can unwind a bit, and this can cause the yolk to settle to one side or another.
So if you are using older eggs--for instance, if you saved some up to use during slow winter laying---it's possible you're just seeing the natural changes that occur to eggs as they age.
The other thing that helps keep the yolk centered is the thickness of the egg white, or albumen. Younger hens have eggs with thicker whites in general. The thick albumen is thicker... and even the thin albumen is thicker than it is with older hens. So as a hen ages, there may be some changes in her egg quality that could cause a yolk to settle to one side.
What that means is that when you use older eggs from older hens, the yolks will probably settle fairly easily.
In addition, hens sometimes lay eggs with watery whites in very hot weather due to the change in the way they breathe (to cool themselves down). That will not be an issue for you if it is not hot outside. But it's true, too, that some respiratory illnesses such as infectious bronchitis can cause a hen to lay eggs with watery whites (thus causing a yolk to settle). If you think that is the issue, you will want to contact a vet or an extension agent to get a diagnosis. We are not vets and can't diagnose your birds. However, if respiratory illness were an issue, you would probably see nasal discharge and see coughing or sneezing.
Aside from the concern of illness, having yolks that settle really isn't a problem for the most part. There are two main occasions where a yolk settling to the side might be a problem. One is when making deviled eggs! It's a pain in the neck to have the white too thin on one side, as it's so easy to tear the white when peeling or just have it collapse. The second is when incubating, since it can cause some problems for the developing chicks. Generally, try to use only your freshest eggs for incubation.