Blessings, Philip, and thank you for the courteous post.
This question right here would deserve a thread entirely on its own if we were to treat the entirety of both Chapters. But to highlight a few passages that explain the correlation and the identifying markers, the parallel to Babylon is based primarily upon the speed with which her judgment comes, as was also the case with Babylon:
8 Therefore shall her plagues come in one day, death, and mourning, and famine; and she shall be utterly burned with fire: for strong is the Lord God who judgeth her. 9 And the kings of the earth, who have committed fornication and lived deliciously with her, shall bewail her, and lament for her, when they shall see the smoke of her burning, 10 Standing afar off for the fear of her torment, saying, Alas, alas that great city Babylon, that mighty city! for in one hour is thy judgment come. (Revelation 18:8-10)
- She is also a city, as was the case with Babylon:
18 And the woman which thou sawest is that great city, which reigneth over the kings of the earth. (Revelation 17:18).
- She will be rich, as was the case with Babylon:
4 And the woman was arrayed in purple and scarlet color, and decked with gold and precious stones and pearls (Revelation 17:4)
- She will practice abominations (sexually licentious religious rites), as was the case with Babylon:
4b. ...having a golden cup in her hand full of abominations and filthiness of her fornication: 5 And upon her forehead was a name written, Mystery, Babylon The Great, The Mother Of Harlots And Abominations Of The Earth. (Revelation 17:4b-5)
- She will murder God's people, as was the case with Babylon:
And I saw the woman drunken with the blood of the saints, and with the blood of the martyrs of Jesus (Revelation 17:6).
- She will practice sorcery, as was the case with Babylon:
23 And the light of a candle shall shine no more at all in thee... for by thy sorceries were all nations deceived. (Revelation 18:23)
- She will be destroyed by violence, as was the case with Babylon:
21 And a mighty angel took up a stone like a great millstone, and cast it into the sea, saying, Thus with violence shall that great city Babylon be thrown down, and shall be found no more at all.
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There are other verses that can be treated in Chapter 18, but these hit the highlights. I'm guessing this might be a question
@Brakelite2 could possibly elaborate on further. Like I said, there is a lot to unpack in Revelations 17 and 18, so it would deserve its own thread. I'm guessing it's more the type of thing he and others might be willing to get into more deeply with you.
But excellent question, Philip, and I do confess it is indeed at the heart of the question. I believe it represents Rome, in particular because of some of the aspects discussed in the OP with regard to Revelation 18:2. But there are other interpretations that have been presented, as you can see just in some of the more recent posts.
God bless.