Middle English titte "nipple of a human or animal, woman's breast," going back to Old English titt, going back to West Germanic *tittōn- (whence also West Frisian tit "nipple, breast," dialectal Dutch titte, late Middle High German zitze), of nursery origin
Note: The Middle English Dictionary lumps this etymon together with the forms under teat, which are likely of Romance origin, as well as including forms deviating from both, as tate and tutes (the latter, from Gloucestershire, apparently reflecting a Mercian Old English form with back umlaut before a geminate according to the Oxford English Dictionary, third edition). The modern use of tit as an impolite word for a woman's breast is first attested in the U.S. in the second half of the nineteenth century; it is not certain if it is a revival of the old word or a completely new formation.