Compare to chepitt (chechepiitt) "covers several things, covers it with a soft object", tuupitt (tetepiitt) "covers with lid, dams up", and uutepitt (uutetepiitt) "covers an object".
Aapitt appears to be a fairly general word, when you are covering up one object, not with a soft object such as a blanket, and not with a lid. However, the aa- at the beginning of verbs like this usually signifies that it applies to "long objects".
The noun 'aapitt (glottal stop added) is a word for "door".