"to sleep lightly or fitfully; fall into a light sleep unintentionally," 1640s, probably from a Scandinavian source (compare Old Norse dusa "to doze," Danish døse "to make dull," Swedish dialectal dusa "to sleep") and related to Old English dysig "foolish" (see dizzy). Perhaps originally a dialect word in English and earlier than the attested date. Related: Dozed; dozing. As a noun, "a light sleep or slumber," from 1731. To doze off is by 1829.
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).