These bags under the eyes or what is referred to as mild swelling or puffiness that occurs under the eyes is usually as a result of old age. It comes as one ages and the tissues surrounding the eyes including the extra ocular eye muscles, gets weaker. This will then cause the normal fat that usually helps to support the eyes to move into the eyelids and cause them to appear puffy. Some fluid can also accumulate in the spaces between the eyes and worsen the swelling.