Dr. Doomsduck said:
WebMD had this to say on the subject:
"While doctors aren't sure of all of the links between breast size and health complaints, they do know that many problems arise from changes in the normal anatomical structure caused by the excess weight on the chest. "As women get older and heavier, their shoulders naturally roll forward, which in turn puts compression in the thoracic outlet -- the area where the ribs, shoulder blades, and nerves come through a rather narrow triangle," says Snodgrass.
That rolling forward, she says, combined with the changes in the anatomic space in the back, compresses nerve fibers enough to cause the pain.
"The larger your breasts are, the more you will pull forward, and the more compression occurs -- and over time that is going to lead to some significant discomfort," says Snodgrass."
Basically, it's not the muscles that cause the pain, but rather the bones in the shoulder that actually shift, so I guess you might be able to prevent it somewhat by compensating your posture in everything you do, but on the long run gravity just sucks.