Bryan Caplan went in search of when, exactly, did the word relationship come into common parlance and makes an educated guess that it happened in the 1970s.
The weird thing is that I can't think of any old-fashioned synonym. Can traditional societies get by with "kinsman," "friend," "ally," and the like without needing any broader category? Or what?
I think, in part, that this is indicative of how much firmer our sense of place was within the myriad of things which we now call relationships. They were once strong and fundamentally part of our identity; we did not need an abstraction so vague that we could apply it to our most beloved as well as our seldom seen acquaintances. Once, the fact that I was the first born in my family would have lent purpose to my entire life; now I live in the chaos of the modern age where blood brother may be friend, enemy, or merely acquaintance.
In short, I think the rise of the term relationship tracks the rise of uncertainty in our familial roles.