Seems to be “musician lingo.” Google’s Ngram viewer has it first showing up in the late 1950s, daddio. A writer on Quora posted in 2014:
I’ve only heard people say in on TV shows/movies. It came up a lot in the Stephen King mini-series Kingdom Hospital. One of the characters was fond of “I do you a solid, and you do me a solid.”
Only if they’re a Geometry teacher.
Hey, do me a squishy and clean up the dog spew.
I hear it in real life, but as in “he did me a solid!” and not as a “request for a solid”
(Yes, I know it’s a slightly older thread). I don’t think I’ve ever heard it on any of the TV shows mentioned, only in real life and occasionally on local radio. I’ve heard it both ways, as in asking for someone for help “hey, can you do me a solid” and as a way of describing someone doing you a big favor, as in “he did me a solid.” I’m not entirely sure whether I use this phrase myself or not. I believe I do, but it’s not a usual part of my lexicon. But I still hear it from time to time and it’s not anything that sounds weird. I don’t remember hearing this expression much myself until probably the late 90s, early 00s.
I say it sometimes.
Without Googling, if I were to guess why solid is being used in this manner-- I would think it stemmed from the word solidarity, somehow.