From more Googling, I've learned that some people think the off in "where do you get off" could possibly be a phonetic сокращение (contraction) for "all of that stuff" ("stuff" here = "nonsense", фигня).

So, "Where do you get off calling Jill fat" might have originally meant "Where do you find such nonsense [= "get all of that stuff"] as calling Jill fat?"

But again, this is only scholarly speculation, and nobody knows for sure.

P.S. However, the more I think about it, the more believable it seems to me that "all of that stuff" could have phonetically mutated to "off", by way of ow-ah-fuff, or something like that.