Yes, tiremakers, especially the largest ones, put a lot of effort into reducing tire weight. They do this to improve performance – a lighter tire is more likely to win a comparison test, as it would provide better longitudinal traction (acceleration and braking), higher lateral grip (cornering), and more agile handling.
Furthermore, lighter tires reduce the overall carbon footprint of the company but also the fuel consumption of the vehicle. This can also lure buyers into buying a tire from a certain manufacturer.
Not to mention, using fewer or alternative materials can sometimes result in cost savings during the manufacturing process, though this is balanced against the costs of research, development, and sourcing of new materials or technologies.