Causes of breast sagging. Aging: As a woman gets older, the ligaments that make up the breast tissue stretch and lose elasticity. As a result, breast fullness is compromised as the underlying support system of tissue and fat diminishes. A change may be particularly evident during menopause. Aug 28, - There are others who only experience weight loss in that area. Why is that? "Genetics “Breast tissue is primarily made of fat,” says Shepherd.