"breast," Old English titt "teat, nipple, breast" (a variant of teat). But the modern slang tits (plural), attested from 1928, seems to be a recent reinvention, used without awareness of the original form, from teat or from dialectal and nursery diminutive variant titties, pl..

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."