Okay - I'll take a shot at this.
[tl;dr: with @rhetorician, I believe "sit" in Rev 17:1 is intended to convey the settledness of a potentate in pomp. This sitting/setting needs to be seen in the immediate context, and in relation to John's use of the Hebrew scriptures.]
Principles for interpretation
This is "Biblical Hermeneutics.SE", though, so I'll start with two general principles for interpreting the book of Revelation (the two most helpful for this question; there are others, of course!), then proceed to apply them to Rev. 17:1, and draw out the nuance that, to my mind, best suits the verse.
- The visions of the book of Revelation are presented in picture language. The details are of interest, however the details often cannot be pressed. This question about Rev 17:1 offers one stark example along the way.
- John of Patmos, presented as our book's author, uses a vast array of traditions from the Hebrew Bible (the Christian Old Testament) with which to paint his pictures. The opening vision of the risen Christ in Rev 1:12-16 is a good example. In those few verses you hear echoes of Exodus, Daniel, Ezekiel, and Zechariah -- it's breathtaking. This is pervasive in Revelation. If we move to a musical metaphor: you can listen to a song with pleasure and be moved, but if you hear in it strains of other music, that experience is deepened. So too with Revelation: catching the resonances of the Hebrew scriptures can deepen our understanding and appreciation of what John is trying to convey. It isn't all about finding his sources though. In G.B. Caird's memorable phrase, often you might as well try to "unweave the rainbow".
It should be obvious that these two principles go hand-in-hand: the palette that John uses to paint his pictures with is the Hebrew Scriptures (less metaphorically, his visions are formed and informed by OT imagery).
Text of Rev 17:1
Just for clarity and ease of reference (English provided is WEB; the NET notes are also handy), even though it's only the last line/phrase or two that we're interested in:
Καὶ ἦλθεν εἷς ἐκ τῶν ἑπτὰ ἀγγέλων τῶν ἐχόντων τὰς ἑπτὰ φιάλας
Kai ēlthen eis ek tōn hepta angellōn tōn echontōn tas hepta phialas
One of the seven angels who had the seven bowls came
καὶ ἐλάλησεν μετ᾽ ἐμοῦ λέγων·
kai elalēsen met’ emou legōn:
and spoke with me, saying,
δεῦρο, δείξω σοι τὸ κρίμα
deuro, deixō soi to krima
“Come here. I will show you the judgment
τῆς πόρνης τῆς μεγάλης
tēs pornēs tēs megalēs
of the great prostitute
τῆς καθημένης ἐπὶ ὑδάτων πολλῶν...
tēs kathēmenēs epi hudatōn pollōn...
who sits on many waters...”
There are three elements in the picture here that constrain how we interpret "sit": (a) the "great prostitute"; (b) her deportment, "who sits"; and (c) "many waters". (I'll worry about the preposition later.) I won't pursue (a) here, but it will intersect with "who sits" and "many waters", as we'll see.
"who sits": Obviously "sitting" is a pervasive, every-day action. But there are a few OT settings that have quite a bit of resonance with our Revelation text:
Isa 47:1, 8
1 “Come down, and sit in the dust, virgin daughter of Babylon.
Sit on the ground without a throne, daughter of the Chaldeans. ...
8 “Now therefore hear this, you who are given to pleasures,
who sit securely, who say in your heart,
‘I am, and there is no one else besides me.
I shall not sit as a widow,
neither shall I know the loss of children.’ ...
This text, like Isaiah 46 preceding it, is about the great reversal of Babylon the splendid being reduced to humiliation in divine judgment. In ch. 47 this is accomplished through personification as a woman. Note especially in the verses cited how this movement is precisely around two kinds of "sitting": the arrogance of Babylon in her pomp (v. 8) shall give way to desolation of sitting in the dust (v. 1).
Other OT texts echo this motif: I'll just mention Ezekiel 23:41 -- another reversal, personification of nation-as-woman, this time the sisters Samaria and Jerusalem, also at the point of self-delusion leading to destruction.
Life is short, so I'll go on to the next item:
You who dwell on many waters, abundant in treasures,
your end has come, the measure of your covetousness.
Babylon is being addressed here, as in Isaiah 47 (notice the pattern). This comes into Greek as kataskēnountas eph' udasi pollois = "dwelling upon many waters". The echo between this text and Rev 17:1 is fairly obvious, but the echoes ripple out.
12 Ah, the uproar of many peoples, who roar like the roaring of the seas; and the rushing of nations, that rush like the rushing of mighty waters! 13 The nations will rush like the rushing of many waters: but he will rebuke them, and they will flee far off, and will be chased like the chaff of the mountains before the wind, and like the whirling dust before the storm.
Not about Babylon this time, but still in Isaiah's foreign nation oracles, this one addressed to Damascus (Syria), if that address is still in force here, later in the chapter. Notice how the "mighty waters" theme mutates into a mountain metaphor around the conglomeration of people who come to destroy.
More widely, the "many waters" motif usually has to do with the roar and power of the primeval sea. This is especially prevalent in the Psalms (see, e.g., 29:3; 77:19, of the exodus waters; 93:4). It is this note that really frames, almost, the whole book of Ezekiel (compare 1:24; 43:2 when the glory of the Lord returns to the renewed temple; via a double-duty literal-metaphorical judgement of Tyre (by the sea) in 26:19). This aspect of the motif also appears in Revelation (1:15; 14:2; 19:6), and in these cases it's the sound that is the important aspect -- just like the Psalms and Ezekiel parallels.
Back to Revelation 17
You'll appreciate that I'm trying to keep this a bit brief (but losing), and there is more to be said about those two OT motifs (I might need to come back for an edit) ... but I think we're in a position to see how these come to bear on Revelation 17, so now it's time for the immediate context.
First, we need to be clear that sitting is not restricted to this occurrence in verse 1:
- 1: the great prostitute who sits on many waters
- 3: a woman sitting on a scarlet-colored animal
- 9: The seven heads are seven mountains on which the woman sits.
- 15: “The waters which you saw, where the prostitute sits, are peoples, multitudes, nations, and languages.”
And to these need to be added one from the next chapter:
- 18:7 For she says in her heart, ‘I sit a queen, and am no widow, and will in no way see mourning.’
The first three in ch. 17 give the woman three different "things" to sit on: the waters (v. 1), the beast (v. 3), the "mountains" (!, v. 9). Only then does John's angel explain what this is about, but by returning to the scenario of v. 1.
This is where the two "principles for interpretation" come back into play. John's vision is a technicolour picture drawn from a set of related OT texts. The details are distinctive even while those distinctions seem not to be of great importance to the vision. Woven into John's vision, though, are elements from both of Jer 51:13 and Isaiah 47.
The amalgamation of "sea" and "mountain" might seem especially strange, but even this is explained by OT usage, where (in a related set of images) the LORD "treads on the backs [al bamothey = waves] of the sea" (Job 9:8), or "treads on the backs [al bamothey = heights] of the earth" (Amos 4:13; cf. Micah 1:3). "Waves" are waters' "mountains", in other words, and YHWH treads on them both. (Hebrew "bamah" is difficult here; see Crenshaw in the bibliography below for the standard treatment of this language.)
Drawing it together
So! With those principles and observations in mind, with (1) and (2) most important for OP:
(1) "sit", then, is echoing especially Isaiah 47, in tandem with Jer 51:13. It's clear that the whore's proud perch is a prelude to punishment. In 17:1, though, she is in her pomp and power. This also explains where the odd "epi" (upon) preposition comes from, and (to my mind) its precise nuance is less important than its scriptural source. There is plenty in in Revelation that doesn't quite make literal sense, and we shouldn't be too literalistic about it. (Maybe that's "Principle for interpretation 3"!)
(2) The broad movement of the chapter, then, is of pride going before the fall, in the most dramatic way. The string of "sitting" references trace this movement. Earlier in Revelation, "sitting" mostly has to do with God (or the elders) on his (or their) throne(s) - e.g. (not exhaustive, there are many!) 4:2-4, 9-10; 5:1; 7:15; 14:14-16; 20:11. This reinforces the impression that Whore Babylon's sitting is hubristic pretension to divine status. (This would require greater space to work out in full, though.)
(3) The "many waters", so often associated with the Lord's coming in majestic power (esp. Psalms, Ezekiel), here further promote the idolatrous presumption of Whore Babylon. It is also a point at which different strands of OT imagery get overlaid, because in Revelation 17, it also resonates with the Isaiah 17 text (cited above) in which this metaphor (some would root it in "myth" - deep mysteries of the supernatural realm) is not only the unruly chaotic force over which the Lord reigns supreme (the pattern in Psalms), but also that threatens to overflow in destructive power on human existence (so Isaiah 17). Both nuances occur here, one in Rev 17:1, the other in its explanation in v. 15.
(4) [Bonus!] The interpretation of 17:15, far from associating a multitude with the people of God (as in Rev 7:9) are those in league with the "ten kings" who turn against "Babylon"(/Rome?). The association of "Babylon" with "Rome" in the symbolism of the vision is fairly widely shared among commentators, and also helps to explain the "mountain" references (around Rome) as pictorial and realistic features coalesce at various points. The emperor in mind is often thought to be Nero, but these things are debated.
That's my take anyway, for what it's worth...
(Very) Select Bibliography
G. R. Beasley-Murray, The Book of Revelation (New Century Bible; London: Marshall, Morgan & Scott, 1978).
G. B. Caird, A Commentary on the Revelation of St. John the Divine, 2nd edition (Black's NT Commentary; London: Black, 1984).
James L. Crenshaw, "wedorek 'al-bamotê 'arets," Catholic Biblical Quarterly 34 (1972) 39-53 [on the motif of the Lord "treading the heights"]
James Moffat, "The Revelation of St. John the Divine", in The Expositor's Greek Testament, ed. by W. Roberston Nicoll (London: Hodder and Stoughton, 1897), vol. 5, see pp. 449-455.