I'm talking about THESE BAD BOYS.
They are so... unweildy. Wouldn't the weight balancing be absolute garbage? And why would you have two heads in the first place?
They did but not in the way you think.
The double headed axe comes from a Minoan object, the Labrys, and as best we can tell it was a religious or symbolic item. Employing a double headed axe on a battle field isn't the best idea, because there is more weight and therefore if you miss your stroke and fail to kill the enemy you are tugged in whatever direction the axe head is going, this is the same reason why war hammers aren't giant (if you want to see for yourself pick up a sledge hammer and give it a swing).
Where double headed axes are actually used is generally in the logging industry. If you take a look at war axes you'll notice that the neck of the axe is relatively thin as throwing axes were sometimes meant to break, while logging axes are thicker and mean to be used for a very long time.
I'm in school now so I can't give you any sources off the top of my head, but I enjoy military history so as soon as I get home Friday afternoon I can consult my library and give you some sources. I hope this helped