The usage of my ass to mean me is now relatively common. My impression is that it originated from AAVE and has since been included in various other dialects. The NGram below implies it became popular in the 70s:
However, that is only for the specific usage of save my ass and might not be representative of the general trend.
So, where does this come from? Does it in fact originate from AAVE or was it just popularized through it? How old is this usage and is there any etymological information on it? Specifically how/why did it enter the general vernacular?
Clarification: This is not about the phrase My ass! to express incredulity in the way expressed by My eye! but about my ass to mean me. As in She saved my ass, or You got my ass into trouble etc.
Best Answer
I watch a lot of westerns about cowboys in the old west (US). It seems to me that there are many references to saving hides (of cattle, also heads of cattle, another way to refer to the number of animals) and conjecture that it's possible that the expression "save my ass" started out as "save my hide". This is the NGram chart that shows the usage overlap:
According to this chart, "save my ass" started to gain in popularity when usage of "save my hide" began to wane.