Where does “Griechin” come from?

Griechin (German) comes from German Grieche, from Middle High German krieche, from Old High German chreah, from Proto-West Germanic krēk, from Latin Graecus, from Ancient Greek Γραικός, from Ancient Greek γραῖα, from Proto-Indo-European ǵerh₂- — to grow old, to mature.

Griechin (German): Greek (female inhabitant, etc., of Greece)

Definitions

Greek (female inhabitant, etc., of Greece)

Ancestry of “Griechin”, step by step

Step	Language	Word	Meaning
1	German	Grieche	a Greek
2	Middle High German	krieche	—
3	Old High German	chreah	—
4	Proto-West Germanic	krēk	Greek
5	Latin	Graecus	Greek, Grecian, of or pertaining to the Greek...
6	Ancient Greek	Γραικός	Greek; a Graecian, a member of an ancient...
7	Ancient Greek	γραῖα	Graea, Boeotia; Greece
8	Proto-Indo-European	ǵerh₂-	to grow old, to mature

Every word from Proto-Indo-European ǵerh₂- →Every word from Ancient Greek γραῖα →Every word from Ancient Greek Γραικός →