1877, "small, tiny; for children," a dialect word, possibly a varied reduplication of wee. Attested earlier (1848) as a noun meaning "a small marble." (Baseball Hall-of-Famer Harold "Peewee" Reese got his nickname because he was a marbles champion before he became a Dodgers shortstop.)
As a type of bird (variously applied on different continents) it is attested from 1886, imitative of a bird cry. Earlier peeweep (1825), and compare peewit.
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Definitions of pewee
small olive-colored woodland flycatchers of eastern North America;