How much do submarines weigh?

It varies with size, not quite exponentially (short of a cubic factor), but much greater than linearly.

The current Virginia class of U.S. attack submarines, nuclear-powered, displace 7800 tons submerged, according to the official U.S. Navy

.

The world's largest submarine, to date, the CIS Typhoonclass, also nuclear-powered, (Depicted as the RED OCTOBER in the movies) displace about 48,000 tons.

The German-designed Type 205 class submarine, diesel-electric in use in several navies displaces about 450 tons.