Where does “aşi” come from?

aşi (Laz) comes from Proto-Kartvelian eks₁w-, from Proto-Indo-European swéḱs — six.

Ancestry of “aşi”, step by step

StepLanguageWordMeaning
1Proto-Kartvelianeks₁w-six
2Proto-Indo-Europeanswéḱssix
Every word from Proto-Indo-European swéḱsEvery word from Proto-Kartvelian eks₁w-