Relatio
Relatio (refero + tio)
1. The laying (of a matter) before the Senate
2. (rhet.) relatio contrariorum, the balancing of opposites
3. Reference (of a thing) to some standard or measure of comparison
4. The action of giving or sending in return
a. the returning (of criminal responsibility) upon one's accuser; the tendering (of an oath) in reply
b. repayment (of a kindness)
5. The relating (of events etc.) in words, narration, recital
6. A figure of speech mentioned by Cicero of uncertain identity
7. (in physical sense) The action of carrying back
source: Oxford Latin Dictionary
I think that the notion of giving or sending in return (meaning 4) is very important. In the texts it is mainly used within the sphere of public life and aims at maintaining balances. Correspondingly on the level of inanimate objects (3) we are guided at the notions of comparison and correlation. On the other side in latin-based languages meaning 5 must have become progressively dominant, and maybe this could (also) be the clue.
Maybe the progress towards the meaning of "relationship" started when relatio stopped having only a pragmatical content and began to include moral and emotional dimensions.
I am not sure, but I think that in latin there is nothing so abstract as "relationship". Usually there is reference to concrete kinds of relationships like amicitia, matrimonium, fraternitas or whatever. Maybe when there emerged the need for an abstract notion including everything, then opened up correspondingly the notion of relatio. This opening must have taken place very late, after the Middle Ages.
Eva Gemenetzis, Latinist