Sound waves do not carry weight in the traditional sense. Weight is a measure of the force exerted on an object due to gravity. However, sound waves can exert pressure on objects they encounter, which can lead to vibrations.
When a powerful sound system produces loud sound waves, the waves create rapid variations in air pressure. These pressure variations cause the molecules in the air to move back and forth, transmitting the sound energy. When the sound waves reach the vicinity of the plastic solo cups and your hair and clothes, the pressure fluctuations affect these objects.
The vibrating solo cups and your hair and clothes are responding to the sound waves by experiencing the pressure changes. The sound waves cause the air molecules around them to oscillate, resulting in vibrations that transfer to nearby objects. The cups and your hair and clothes vibrate because they are sensitive to these pressure fluctuations.
It's important to note that the vibrations caused by sound waves are relatively small and do not generate a significant amount of force. The perception of vibration in objects and materials around a loud sound system is primarily due to the sensitivity of those objects to air pressure changes rather than the sound waves having any substantial weight.