Gaia Falls is the name of the location where Weyard's oceans pour into the void. The name Gaia Falls does not entirely represent the border between Weyard and the void, but is used to describe the massive waterfalls falling into the void.
The oceans do not seem to run out of water despite the fact that Gaia Falls is a huge waterfall constantly pouring countless gallons of Weyard's water into the void. Also, despite the fact that Gaia Falls are a huge drop that is likely to have a strong current, in Golden Sun: The Lost Age, your ship does not get pulled over the edge into the abyss, nor can you sail your ship over the edge, though this is probably just a gameplay mechanic to allow ease of navigation, as in-game NPCs mention that the currents near Gaia Falls are indeed swift and very dangerous.
Absence of AlchemyEdit
Because of Alchemy's disappearance, the Gaia Falls are constantly growing inwards as the world's edge crumbles and falls into the void. Many settlements are in imminent danger of falling into the void, including the Apojii Islands and the SW Atteka Islet, but more notably Prox (and critically, the Mars Lighthouse) in the north. The Proxians are aware of this and it is their motivation for their actions throughout the games. By lighting the Elemental Lighthouses, the power of Alchemy would be released and prevent Gaia Falls from growing, which is the primary goal of Felix and his companions in The Lost Age.
Return of AlchemyEdit
The concept is similar to the belief held by ancient civilizations that the earth is flat. Until the discovery that the world was round, humans believed that, if they sailed far enough, they would simply drop off the world's edge.