1550s, possibly an alteration of tip for tap "blow for blow," from tip (v.3) "tap" + tap "touch lightly." Perhaps influenced by tit (n.2).
Entries linking to tit for tat
tip v.3
c. 1200, "to strike, occur suddenly," of uncertain origin, possibly from Low German tippen "to poke, touch lightly," related to Middle Low German tip "end, point," and thus connected to tip (n.); or else related to tap (v.1). Meaning "strike sharply but lightly" is from 1560s. Sports sense is from 1816, originally in cricket. Related: Tipped; tipping.
tap v.1
"strike lightly," c. 1200, from Old French taper "tap, rap, strike" (12c.), from a Gallo-Roman or Germanic source ultimately imitative of the sound of rapping. Meaning "to designate for some duty or for membership" is recorded from 1952, from notion of a tap on the shoulder. Related: Tapped; tapping.
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."