1610s, from grime + -y (2). "App[arently] not in literary use during the 18th c." [OED]. Related: Griminess.
Entries linking to grimy
grime n.
1580s, of uncertain origin, probably alteration of Middle English grim "dirt, filth" (early 14c.), from Middle Low German greme "dirt" or another Low German source, from Proto-Germanic *grim- "to smear" (source also of Flemish grijm, Middle Dutch grime "soot, mask"), from PIE root *ghrei- "to rub." The verb was Middle English grymen (mid-15c.) but largely was replaced early 16c. by begrime.
-y 2
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.