|This article contains huge spoilers!|
Noelia gathers Doom Stones throughout the story and later reveals in Crankshaft's Workshop that "once the negative energy has left a Doom Stone, [her] powers should be able to return it to the sky." Her plan is to make a Floatstone out of Doom Stones. She wants to do this so that she may find and visit Levitania because that is where her mother may have lived as Noelia has learned in an old Port Puerto tale.
In Chapter 6, Larkin reveals that he has discovered notes in an abandoned shack which stated that Levitania was being purified over time and that "new Floatstones are forming in old soil layers." This explains how Levitania is able to float in the sky. Robin then loads his ship up with the giant Floatstone found in West Levitania to bring it back down for the player to drop off at Castele Castle.
The giant stone is later used to power up the Goddess's Ship.