There are two varieties of Eye-Bats: those from Gravity Falls and the ones from the Nightmare Realm. Eye-Bats from Gravity Falls have black wings and are as large as regular bats, while Eye-Bats from the Nightmare Realm have red wings and are larger than a human. Aside from their wings and size difference, both have a yellow eyeball.
Normal Eye-Bats mostly just fly around and avoid humans. Eye-Bats from the Nightmare Realm can project a red light they use for security, freezing people into stone and take them away.
They are revealed to be working for Bill Cipher and his demon pals in "Weirdmageddon" where a number of Eye-Bats turned people into stone then capture and take them to the Fearamid, the whole downtown of Gravity Falls was covered with Eye-Bats flying around the openings surveying the areas for civilians. During the final battle at least a few Eye-Bats are destroyed by the Shacktron robot.
Later, the remaining Eye-Bats that were left over are cowardly chased out of the barn owned by Sprott, sometime after the end of the event.
Wendy on an Eye-Bat.
A number of Eye-Bats patrolling Gravity Falls.
An Eye-Bat get blasted by Rumble.
An Eye-Bat petrifying a raccoon at the Mystery Shack.