"breast," Old English titt (a variant of teat). But the modern slang tits (plural), attested from 1928, seems to be a recent reinvention from teat, used without awareness that it is a throwback to the original form. Titty, however, is on record from 1746 as "a dial. and nursery diminutive of teat."
1540s, "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 (cf. 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," usually in deprecatory sense of "a hussy, minx" (1590s).
A woman's breast: She couldn't make it out there. No tits
Related Termscold as hell, get one's tail in a gate, suck hind tit, sugar tit
[1928+; a respelling of teat]