"Pay her back even as she has paid, and give back to her DOUBLE according to her DEEDS;
This is consistent with the judgment awarded in crimes where "breach of trust" has been committed (Exodus 22:1-4-7-9). Obviously, the Babylonian evil system is very corrupt at this time and trust is nonexistent. Interestingly, the crimes are so disguised as pleasure that when they are committed they don't appear to be "payment". If one listens to advertising, you hear phrases such as "you earned it", "wouldn't you look good in .....", or "everyone else is doing it (so it must be OK, implied)". But it really is an evil payment.
From a spiritual viewpoint, this is the repayment the martyrs sought (Revelation 6:9-10). The martyrs asked when this would happen; here in chapter 18, the time has come.
As for God's chosen people, this payback is prophetically described in Jeremiah 51.
in the CUP which she has mixed, mix twice as much for her.
So deep is the evil in the world during these times that to extract the "proper vengeance" (Romans 12:17-21) from Babylon, the judgment is doubled. As a sidelight to the Romans passage, the "evil" is to be overcome with GOOD. This is not GOOD done by the few believers who remain and have not been martyred, but rather this is the GOOD that is God (Luke 18:18-19-30). It is the GOOD of which humans gained knowledge by eating/internalizing the fruit of its tree (Genesis 3). We don't know what happens to the tree of the knowledge of GOOD and EVIL after the Genesis incident. However, one could imply that the tree of the knowledge of GOOD and EVIL is finally removed or destroyed at this time. That is, the double portion of judgment (the GOOD) overcomes the EVIL she has mixed in the same CUP.