"small," 1883, baby-talk from plural of bit (n.1) or a variant of bitty (q.v.).
Entries linking to bitsy
bit n.1
"small piece," c. 1200; related Old English bite "act of biting," and bita "piece bitten off," which probably are the source of the modern words meaning "boring-piece of a drill" (the "biting" part, 1590s), "mouthpiece of a horse's bridle" (mid-14c.), and "a piece (of food) bitten off, morsel" (c. 1000). All from Proto-Germanic *biton (source also of Old Saxon biti, Old Norse bit, Old Frisian bite, Middle Dutch bete, Old High German bizzo "biting," German Bissen "a bite, morsel"), from PIE root *bheid- "to split."
The meaning "small piece, fragment" of anything is from c. 1600. The sense of "short space of time" is 1650s. Theatrical bit part is from 1909. The colloquial sense of "small coin" in two bits, etc. is originally from the U.S. South and the West Indies, in reference to silver wedges cut or stamped from Spanish dollars (later Mexican reals); transferred to "eighth of a dollar."
bitty adj.
"small," 1898, baby-talk, from bit (n.1) + -y (2). Earlier "made up of little bits," 1873.
itsy-bitsy adj.
"charmingly small," 1882, from itty (baby-talk form of little) and/or bitsy. Bitsy-itsy is recorded from 1875. Itty-bitty from 1849; tiddy-itty from 1852.
The fond old captain used to talk of her very much as if she were six months old, and fractions in teething, calling her his Peetums-keetums, his Pitsy-itsy-kitsy and such like, which annoyed the girl, .... ["M.B.," "John's Wife," in "Tales of the Day," 1861]