Of course, after a certain size, this increase ceases and the visibility circle stops expanding. The first obvious point is altitude. The higher the island, the more visible over the horizon. In fact, many islands were discovered that were initially described as being very small and then only later realized, once the ship grew closer, that the initial description had covered only the tops of volcanoes. The second point is not as obvious.
Larger islands have their own microclimates which can produce low-lying fog.
This fog can sometimes be seen at a greater distance than the island itself. In addition, cloud cover even at great altitude can sometimes hint at the presence of an island. Next, there are animals. Many birds will fly far from land, heading out to sea. If the gamemaster has created a world with such birds, the characters may be able to determine their distance from an island based on which birds they can see and in which direction they are seen.