Sound waves themselves do not carry weight in the sense of having mass. Sound is a mechanical wave that propagates through a medium, typically air, but it can also travel through other materials like water or solids. While sound waves don't have physical weight, they do exert pressure on objects they encounter.
When you stand near a powerful sound system, the vibrations you observe in the plastic solo cups, your hair, and your clothes are a result of the sound waves interacting with the surrounding air and objects. Sound waves consist of compressions and rarefactions, regions of increased and decreased air pressure respectively.
When the loud sound waves pass through the air, they create alternating regions of high and low pressure. These pressure variations can cause objects in the vicinity to vibrate. In the case of the plastic solo cups, the sound waves may be strong enough to induce vibrations in the cups, causing them to move or shake. Similarly, your hair and clothes can vibrate due to the pressure fluctuations in the air caused by the sound waves.
It's worth noting that the intensity of the sound, as well as the distance from the sound source, can influence the magnitude of the vibrations. The closer you are to the sound system, the more pronounced the effects are likely to be.