What does "To weep into stones are fables" mean?

According to one version of the book with footnotes, this refers to the fable of Niobe:

Devastated, Niobe fled back to Mount Sipylus and was turned into stone, and, as she wept unceasingly, waters started to pour from her petrified complexion.

https://en.wikipedia.org/wiki/Niobe

Compare with the quotes here: https://www.dictionary.com/browse/niobe

As @Laurel correctly put it, it is a reference to the fable of Niobe.

Fables are fictional stories. So the phrase 'To weep into Stones are fables' is alluding to the fact that things that are impossible to happen are merely told in fables and are not realities. (It is impossible for stones to weep. In the fable of Niobe, not only did she turn into stone, her incessant weeping still continued after her petrification)