Middle English word eem comes from Proto-Germanic *haimaz (Home. House. Village.), Proto-Indo-European *h₂ewh₂-

Detailed word origin of eem

Dictionary entry	Language	Definition
*haimaz	Proto-Germanic (gem-pro)	Home. House. Village.
*h₂ewh₂-	Proto-Indo-European (ine-pro)
*awô	Proto-Germanic (gem-pro)	Grandfather.
*awahaimaz	Proto-Germanic (gem-pro)	Maternal uncle.
ēam	Old English (ang)
eam	Middle English (enm)

Words with the same origin as eem