They were already using a 1/4 inch steel plate as an underbody shield but it wasn't strong enough to prevent piercing and fires in certain situations.

Apparently the people at Tesla calculated that the cost of adding these plates was worth the benefit of improved consumer protection and good publicity.

Weight is not an issue for this part because it actually helps further lower the cars center of gravity.

I wish my car had a titanium underbody, that would simply be badass.