Back pain may or may not be related to the large breasts, but large breasts can certainly put strain on the back. A breast reduction may or may not improve your symptoms.
The normal range of breast sizes is A - B - C cup size. In effect the female chest seems to be built to accommodate breasts in that size (and attendant weight). D cup and larger size breasts are outside the normal range and can cause problems with or without the support of a bra. Like most things it's usually better tolerated when young, but strain on the back, spine, and neck generally eventually cause problems. Sometimes volume can be more fatty than glandular. Fat is relatively light -- floats on water -- glandular breast tissue is heavy. There is some debate on how much beast implant volume/weight adds to this problem. Another factor is the contribution of sagging of the breast off the base. Another is activity level. Women in sports usually don't want breasts larger than an average B cup.
