It is the amount of fatty tissue that makes some breasts bigger than others. In other words, the milk producing apparatus is about the same in both small and big breasts. Therefore breast size is not linked to the ability to produce breast milk and breastfeed per se. Even flat-chested women, who don't have practically any fat cells in their breasts, can breastfeed. Besides, you really don't know your final breast size until after your first pregnancy, because the milk-producing cells and milk ducts grow and branch out a lot during the third trimester.
However, breast size does affect the breastfeeding relationship in at least two different ways. First of all, many times the babies of large breasted women have some difficulty in latching on in the beginning because they have such a tiny mouth in comparison to the areola they are supposed to take into their mouth and suck on. This problem usually goes away as the baby grows older. A lactation consultant can help with the initial problems; for example, the mother can pump the milk during the early weeks while the baby is learning a proper latch, and the pumped milk can be fed to the baby in a bottle.
Secondarily, the research of Peter Hartmann has shown that the milk storage capacity varies a lot between women. Breast milk is produced continually and it accumulates in the milk ducts between feedings. During feeding, a baby typically empties about 70-80% of the milk in the breast. Hartmann found in his studies that some women had 3 times as big a storage capacity than others - but that all of them produced the same amount of milk over a 24-hour period. In general, bigger breasts of course would have a bigger storage but it was noted that breast size was not always a good predictor of production or storage capacity.
In practical terms it means that women with small storage capacity breasts need to nurse more often, and the babies take in less per feeding. Women whose breasts have a larger storage capacity can 'deliver' more milk in one feeding, and so the baby needs to nurse fewer times per day. This further confirms the need of cue feeding or demand feeding where the baby sets the frequency of breastfeeding - and not the clock or the pediatrician or the grandmother.
Breast size in pregnancy, breastfeeding, and weaning
During pregnancy, breasts grow a lot in size. This is due to the growth and development of the milk glands. Fat actually goes away from breasts at this time, as the milk glands "fill" the breast. The areola darkens considerably, and breasts already start producing colostrum.
The "peak" size is usually reached when the mature milk comes in about 3-5 days after delivery. At this time most women experience some engorgement, which goes away in a few days. Then, once the breastfeeding relationship is established, breasts will constantly keep changing their size a little bit, as the baby empties the breast, and as milk is constantly being made in the alveoli (milk glands) to fill the breast.
With weaning, when the milk is no longer needed, the milk glands atrophy or shrivel up. The breasts will then shrink in size. If the weaning was abrupt (cold-turkey), this shrinking can be quite marked. However, that is not the end of the story. After weaning, over a period of up to 6 months, the body deposits fat back to the breasts. With gradual weaning, often there isn't any abrupt change in breast size, but the fat-depositing process can take place at the same time with the slow weaning.
With this process of "refilling" with fat, the breasts often end up about the same size as before pregnancy, though they may be hanging down more (saggier). However, some women's breasts do stay smaller than they were before pregnancy. See also Do breasts shrink after weaning?
Hypoplastic tubular breasts (insufficient glandular tissue) linked with low milk supply
There is one exception to the rule about breast size/shape and breastfeeding ability, and that is that few women have insufficient glandular tissue (IGT) in their breasts. In other words they simply don't have enough milk producing cells, and these women can then experience milk supply problems. This condition is also called breast hypoplasia, hypoplastic breasts, or underdeveloped breasts. You can see many pictures of women with IGT at this link.
This kind of breast is underdeveloped (hypoplastic) in terms of the milk glands. They lack normal fullness and may look like 'empty sacks', and may seem bulbous or swollen at the tip. Many times hypoplastic breasts are widely spaced from each other, and narrow at the chest wall. Due to lack of glandular tissue, they have an elongated or tubular form, and often are quite small. The areola can be enlarged. There may be a significant asymmetry. The breasts don't grow during pregnancy and there is no engorgement when the milk is supposed to come in after giving birth.
Scientists don't yet know for sure the reason(s) for this underdevelopment. One theory is that at least in some women it would be linked to too little progesterone, since progesterone mediates the growth of alveoli (milk making glands).
In a 2006 study in Mexico, teenage girls who lived in the agricultural valley with heavy pesticide use had poor mammary gland developmend, and 18.5% of them had NO milk glands.
Other issues include PCOS and other insulin metabolism issues, hypothyroidism, and testosterone overload. Fixing the metabolic issues may help, as might pushing lots of stimulation to increase prolactin levels after birth.
There is also one interesting case reproted in the medical literature where a woman with such underdeveloped breasts was able to successfully nurse her second child, after being given natural progesterone during her second pregnancy. Progesterone stimulates the growth of the glandular tissue in breasts during pregnancy.
If you happen to have these tubular hypoplastic (under-developed) breasts, talk to a lactation consultant before giving birth. Even better, talk to a doctor before pregnancy about a possible natural progesterone treatment. There are measures you can take to try increase your milk supply and your chances of breastfeeding, such as
• have an unmedicated birth if possible, and put the baby to the breast right after birth
• nurse often and on cue
• start to pump about three days after birth
• try the herbs fenugreek and blessed thistle or the drug domperidone
• breast compression technique to stimulate more letdowns
• Correct underlying metabolic or hormonal issues (PCOS, hypothyroidism). One lady has posted her success story below; she was able to see breast changes during her 2nd pregnancy and subsequently breastfeed, after taking Metformin to correct her PCOS.