After breast augmentation, swelling "drops" to the tummy and hips by gravity (when you are standing, which is most of the day), but it also drops to the sides and back (when you are laying down, which is the rest of the day). The interstitial fluid that is responsible for every patient's swelling and discomfort gradually reabsorbs and the kidneys eliminate it. You note this as softening of the breasts, and reduction of the swelling wherever it is.
Realize that the swelling and fluid that goes to the back when you are reclining or asleep then drops to the mid and lower back as you stand, so this is truly common, normal, and in the absence of OTHER symptoms (like chest pain or shortness of breath), nothing to worry about.
In addition to the fluid/swelling discussion above, there ARE shifts of balance points and center of gravity that your core muscles accommodate to over time. Compensation for sore chest muscles can contribute to back pain as well, and this resolves as the chest muscles heal. This continues to settle as you resume normal activities and exercise all of your muscles!