The phrase tit for tat means an equivalent given in return or retaliation.

The expression seems to be a variation of the obsolete and more comprehensible tip for tap, in which both tip and tap meant a light but distinct blow, stroke, hit. The phrase therefore meant blow for blow.

The words tip and tap first appeared combined in Fortunes Stabilnes, by Charles d’Orléans (1394-1465).

Context: the letter patent that sets out the feudal arrangement between the lord, Love, and the retainer, the lover, has just explained to the latter that the higher women are set in nobility, the more carefully he should control his behaviour. The lover is now told:

But, what, a cherlis doughtir dawbid in clay
As strokis grete (not tippe nor tapp, do way!),
But loke who that most fowlist kan bigynne
The rewdisshe child so best lo shall he wynne.
translation:
But you can win a churl’s daughter bespattered with dirt by using heavy blows (don’t bother with mere tips and taps!), but whoever begins does it most harshly so that he best obtains the uncouth girl’s affection.

The phrase tip for tap itself is first recorded in A hundreth sundrie flowres bounde vp in one small poesie (1573), by the English soldier and poet George Gascoigne (died 1577):

Much greater is the wrong that rewardeth euill for good, than that which requireth tip for tap.

The English poet and playwright William Shakespeare (1564-1616) used the variant form tap for tap in The Second part of Henrie the fourth, continuing to his death, and coronation of Henrie the fift. With the humours of sir Iohn Falstaffe, and swaggering Pistoll (around 1597):

(Quarto 1, 1600)
– Lord Chief Justice: What foolish maister taught you these manners, sir
Iohn?
– Falstaff: Maister Gower, if they become me not, hee was a
foole that taught them mee: this is the right fencing grace, my
Lord, tap for tap, and so part faire.

The form tit for tat is first recorded in The Spider and the Flie (1556), by the English playwright and epigrammatist John Heywood (1497?-1580?):

If (quoth the butterflie) the flies do here pike [= pick]
That quarell to spiders, in customes vsacion [= usage].
That is tit for tat, in this altricacion [= altercation].

Both tit and tat refer to touching lightly, patting, but onomatopoeia and alliteration play the important role, as can be seen in the couplet from a song apparently current when the English playwrights Thomas Dekker (circa 1572-1632) and John Webster (circa 1580-circa 1634) quoted it in North-ward hoe (1607):

– Doll: Come tit mee, come tat mee, come throw a kisse at me, how is that?
– Captain Jenkins: By gad I kanow [sic] not, what your tit mees and tat mees are, but mee uatha — Sbloud [= ’sblood = God’s blood] I know what kisses be.

The phrase tit for tat used to be part of a rhyme, as A. De Morgan explained in Notes & Queries (2^nd series, vol. 12, July-December 1861):

If we do not look after a proverb, it is sure to be cut down, if it will bear shortening. What has become of the rest of “tit for tat”? When I first heard the saying, it ran thus:
“Tit for tat,
Butter for fat;
If you kill my dog,
I’ll kill your cat.”*
But I can find nobody nowadays who remembers having heard the whole.

(* cf. also cowardy, cowardy custard)