The Collaborative International Dictionary of English v.0.48:

Bubby \Bub"by\ (b[u^]b"b[y^]), n. [Cf. Prov. G. b["u]bbi, or It.
   poppa, Pr. popa, OF. poupe, a woman's breast.]
   A woman's breast. [Low]
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Bubby \Bub"by\, n. [A corruption of brother.]
   Bub; -- a term of familiar or affectionate address to a small
   boy.
   [1913 Webster]