So what was the path by which this word, originally meaning fairness or equality, came to mean “the value of an ownership interest in property, including shareholders’ equity in a business”?
It’s from the sense (OED definition 5) “An equitable right, i.e. one recognizable by a court of equity.” This is subentry 5c (orig. U.S.); the first cite is:
1904 E. S. Meade in Polit. Sci. Q. Mar. 50 Its preferred stock is quoted at..prices which indicate a general conviction that the equity in the company is worth little.
In essence, it seems to be an extension of the concept of “fairness” to “fair share” and thence to “value of one’s share”.
Well said, Doc.