Oh, I just love the etymology on this one. See, worth comes from the Old English weorð (that funny symbol is a now unused letter for the “th” sound), meaning “equal in value”, about the same as we have. Weorð in turn comes from the Proto Germanicwerthaz, which actually means toward or opposite. It might seem weird, but if you think of it in the sense of opposite and equivalent to, it makes more sense.
What you might not know is that there’s another worth, a homophone/graph that has quite a different meaning. Instead of value, this worth means “to come to be” and is now rarely if ever used. It has a slightly different etymological line, coming from the Old English weorðan instead of weorð (so, something like “worthan”) and the Proto Germanic werthan, which means “to become” and which itself came from the above werthaz.
It gets interesting when you look at the history of werthaz. That word is thought to come from the Proto Indo European wert, turn or wind, which comes from wer, meaning bend. And that’s also the distant ancestor of versus, of all words, and with quite a different ancestry.
Versus showed up in the mid fourteen hundreds and instead of Germanic origins, came from the same word in classical Latin, where it means “turned against”. And the Latin versus, which comes from vertere, or “to turn”, can be traced to the Proto Indo European wert as well.
TL;DR: worth and versus are thought to come from the same word, through Germanic and Latin lineages, respectively.
Tony Jebson’s page on The Origins of Old English