Well you done done me and you bet I felt it
— Jason Mraz, I'm Yours
What does the first sentence from this song mean?
You done me - to do someone: You had sex with me
You done me in - to do one in: to "kill" someone - You had a big impact or killed me
You done me wrong - to do someone wrong You cheated on me
When you are done doing me, you done done me.
The first part of the sentence can be translated as, "you have done me," where "done" is quite possibly sexual :-)
The second part indicates that this had a positive impact, rather than that the singer just noticed this happening.
The final two words indicate the singer has been won over, probably through being impressed by the aforementioned activity.
...where (as in OP's example) standard English would either discard the first "done", or replace it with "have" (the meaning is identical either way).
Thus the first "done" is simply a dialectal way of indicating/intensifying the past tense aspect of the second occurrence. It's Off Topic (lyrics interpretation) to speculate on what exactly the second "done" means, but my guess is "had a big effect on me".