Green’s Dictionary of Slang

berkeleys n.

[Rom. berk, breast]

the female breasts.

[UK]Farmer & Henley Sl. and Its Analogues I 180/2: Berkeleys, subs. (common).—A woman’s breast. (It may be noted that in the gypsy, berk, or burk = breast; plural, berkia.
[US] (ref. to 1890s) H. Rawson Dict. of Invective (1991) 387: Among the others in this collection [F&H]: bubbies, charlies, blubber, butter-boxes, berkeleys, diddies, globes, dugs, and ‘charms’.