Tinguian (Northern Luzon) folklore (oral tradition) describes the headaxe and its uses in many ways. It also mentions several times the headaxe being used magically by a character in the stories to cross bodies of water or the sea.
This leads me to conjecture that the crescent-shaped blade may have been inspired by the shape of a boat
More conjectures .... The shape may have originated from the coastal lowlands (not the mountains of the Cordillera where there is no sea) of Luzon, and where blacksmithing technology (using the Malay forge) may have entered the island.
Nonoy