What controls the size of breasts?
The known factors seem to be mainly oestrogen and genetic (although I haven't been able whatsoever to find detail on what genes):
Manning et al (1997): Breast asymmetry and phenotypic quality in women. Evolution and Human Behavior, 17 (2): 129–143.

Our data support the thesis that mammotropic hormones, particularly estrogen, are harmful because they suppress the immune system. Heavy women with high levels of body fat produce more estrogen and, therefore, bigger breasts. However, more estrogen leads to an increase in breast asymmetry. Women with “good genes” are able to produce symmetric breasts despite the presence of large quantities of estrogen. Large and symmetric breasts are therefore honest signals of high phenotypic quality in women.