Dark puffy bags under the eyes are often caused by a weakening of the muscles and tissues around the eyes. As the supporting muscles weaken, the fat can move into the lower eyelids. This is common among older people and appears as puffiness or mild swelling under the eyes.
Fluid accumulation in the area underneath the eyes can add to the problem, although this is generally not a serious medical issue. While cosmetic treatments may help with puffy bags under the eyes in some cases, home remedies, such as a cold compress, can also help relieve the swelling and puffiness.