Weights are sometimes used in BDSM in a variation of sensation play. In its perhaps most common form, small weights are attached to a woman's clitoral lips or to her nipples. This creates a pulling sensation. When attached to her clitoral lips it's usual for her to be bound to a vertical frame or to anchor points on a wall with her legs apart. When attached to her nipples she may be bound in a sitting or standing position, or may be slightly leaning forward.
To increase or change the sensation her top or dominant may pull on the weights or may start them swinging them back and forth. When the weights are heavy they may be painful and swinging them becomes a way of inflicting torture.
Males also can have weights attached to their penis or testicles.
Many sex shops and speciality BDSM suppliers will have a range of weights custom made for dangling off genitals and nipples. These are usually attached using nipple clamps.
Attaching weights to nipples and clitoris lips, as noted, usually involves clamps. These work by squeezing folds of flesh between their jaws and this flesh has most of the blood squeezed out of it as a result. This state can only be safely maintained for a short period of time (measured in minutes), after which permanent damage may occur. Never leave clamps attached for too long.