... she's given up years ago, years ago...
I think it can be explained by the semantic intent of "years ago, years ago". The speaker isn't placing the act of giving up smoking on a historical timeline, saying when it happened, as much as she is indicating for how long her sister has remained a non-smoker since giving it up. In the sentence immediately preceding, the focus is on for how long one can remain smoke-free without backsliding.
This duplication of "years ago, years ago" is related to the colloquial flourish of repeating something to make it more extreme:
They lived in a big, big house.
There was this teeny, teeny crack in the windshield that became a very large crack.