You can own a beer, or you can owe someone a beer. These are approximately opposite statements of your wealth (in beer).
I can see some references that both are "From Middle English owen, from Old English āgan" (owe, own) but that doesn't really explain how the modern words came to be as they are.
Since "owe" and "own" share a common root or origin, how did they come to have such a distinction?
Based on the etymology of the Old English āgan that both words derive from, it seems that at that time it could mean either to own, or to cause someone else to own. Thus "I āgan a beer" - I own a beer, it belongs to me. "I āgan you a beer" - I will make you own a beer, I will make this beer belong to you. The words aren't all that different, then - "I owe you a beer" is basically similar to "I will make you own a beer".
