1630s, probably from dialectal tid "fond, solicitous, tender" (perhaps by influence of tit (n.2)) + bit (n.1) "morsel."
Entries linking to tidbit
tit n.2
1540s, a word used for any small animal or object (as in compound forms such as titmouse, tomtit, etc.); also used of small horses. Similar words in related senses are found in Scandinavian (Icelandic tittr, Norwegian tita "a little bird"), but the connection and origin are obscure; perhaps, as OED suggests, the word is merely suggestive of something small. Used figuratively of persons after 1734, but earlier for "a girl or young woman" (1590s), often in deprecatory sense of "a hussy, minx."
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."