From contributor TC:
3/4" (2cm) needs a plywood underlayment for support. This method is mostly used on the West Coast. On the East Coast, 1 1/4 (3cm) is common. 3cm is considered strong enough to not require an underlayment and is not used. As far as cantilever amount, it is generally given that 3cm can go 12" without support, you would need to check with your fabricator as far as how far he's willing to go.

As far as final cost, because 3cm slabs do not need to be laminated on the front, there is less work involved, so the cost difference between 2cm and 3cm material is usually minimized.