It doesn't cost anything persay, but if you have a limited data plan (as opposed to an unlimited one) it will use alot more data then you may be used to.
And yes Verizon has the ability to tell if you are tethering, and can back charge you via a hefty per mb fee. Are they likely to do this? no probably not. It happens very very infrequently, we don't believe that Verizon as a matter of policy does checks on your account for potential unauthorized tethering but it is within the realm of possibility.