John Gill, on Jer 51:62

And thou shall say,.... Not only use the above sign and ceremony, but explain the meaning of it to those of his friends who might accompany him; and what he said was in the name of the Lord, as the form and manner in which the following words are delivered show: thus shall Babylon sink, and shall not rise from the evil that I will bring upon her; as this book, with the stone bound to it, does, and shall no more rise than that can; the evil of punishment brought on Babylon will sink her to such a degree, that she will never be able to bear up under it; but be so depressed by it as never to rise to her former state and grandeur any more: and they shall be weary; the inhabitants of it, and have no strength to resist their enemies; or, rather, shall be so weak as not to be able to stand up under the weight and pressure upon them, but shall sink under it; or shall weary themselves in vain to preserve their city from ruin, or restore it when ruined; see Jer 51:58; thus far are the words of Jeremiah; that is, concerning the destruction of Babylon, as is said concerning Moab, Jer 48:47; for what Maimonides (m) says, that though Jeremiah lived some time after, yet ceased to prophesy; or that, when he had finished his prophecy concerning Babylon, he prophesied no more, is not true; for it is certain that many of his prophecies were delivered out after the date of this, though this is recorded last: or the sense may be, thus far are the prophetic words of Jeremiah; and so the Targum, "hitherto is the prophecy of the words of Jeremiah;'' what follows in the next chapter being historical; for there is no necessity to conclude from hence that that was wrote by any other hand; either, as many have thought, by Ezra; or by the men of the great synagogue, as Abarbinel. (m) Moreh Nevochim, par. 2. c. 45. Vid. Kimchi in loc. Next: Jeremiah Chapter 52