Where does “κωνώπιον” come from?

κωνώπιον (Koine Greek) comes from Ancient Greek κώνωψ, from Ancient Greek φάγος, from Ancient Greek φαγεῖν, from Proto-Indo-European bʰh₂g-, from Proto-Indo-European bʰeh₂g- — to divide, distribute, allot.

Ancestry of “κωνώπιον”, step by step

Step	Language	Word	Meaning
1	Ancient Greek	κώνωψ	gnat, mosquito
2	Ancient Greek	φάγος	glutton
3	Ancient Greek	φαγεῖν	aorist active infinitive of ἔφαγον
4	Proto-Indo-European	bʰh₂g-	—
5	Proto-Indo-European	bʰeh₂g-	to divide, distribute, allot

Every word from Proto-Indo-European bʰeh₂g- →Every word from Proto-Indo-European bʰh₂g- →Every word from Ancient Greek φαγεῖν →