Is it not normal for the yolk to be closer to one side? The yolk has a difference viscosity and specific gravity compare the the egg white, so I thought one sinks to the bottom while the other floats on top like mixing oil and water. If the egg is on its side in the pot as it boils, the yolk would sink to the bottom, then as the egg solidifies, it would appear to be on the side when you hold the egg with the pointed end up or down.
Older eggs will have had more time for air to permeate the shell and as the contents of the shell condense, it leaves an air pocket inside the egg. Sitting these older eggs in water will cause the air pocket (wide end of the egg) to try to float up, making the egg stand on the point. This allows the yolk to settle more in the middle of the egg white. If the eggs are old enough to float all the way up off the bottom of the pot, they may be too old for consumption. I date all my eggs that I collect because I sell them. Of the ones I save for my family, I usually set eggs aside for a minimum of 3 weeks before boiling them. It lets the contents condense and it also keeps the membrane from sticking to the shell and tearing the egg apart when I peel it.