My best guess, and that's all it is:
There is a figure of speech I've heard often enough to think it's popular, at least regionally, "Shit weasel." Stephen King used it as the name of his rectally explosive monsters in Dreamcatcher.
I think "me-weasel" is an expression of Dresden's self hatred bleeding into his humor, as is common with seriously depressed people who crack jokes constantly. I have a brother who does this, he casually drops self loathing and suicidal ideation into his off-the-cuff banter, and I don't think it's intentional. I think it's something that feels so normal and correct that it bleeds through even when you don't mean it to, or even think about what you're saying. There's a reason people can pretend to be psychic and do mentalism tricks, most folks have no idea how much of themselves they're expressing.
Dresden takes it entirely for granted that Ramirez will know "me" means the same thing as "shit."
But that's just my impression. It could be that I missed something that makes it a callback. Just can't think what it would be.
