First the basics. 2cm is a little more than 3/4" and 3cm is a little less than 1 1/4". Most people getting 2cm counters have a strip laminated where the edge is visible not for structural integrity but to make the stone look twice as thick. This is also done with 3cm granite, but to a much lesser extent as the granite has a thicker appearance already. Most 3cm counters are not laminated. Most. I have seen 6cm, 8cm & 9cm thicknesses as laminations are built up. Anything is possible in our world.
Properly installed you will not get stress cracks with either unless you abuse it. If you have a dance contest on your countertop and it cracks it is not the fault of the stone or the installer. When you do an install there is always something underneath the slab supporting it. Sometimes it is a full substrate of plywood or a cementuous backer like hardibacker. Other times the granite slab is merely glued with silicone to the front edge, the back edge and the cross ribs of the cabinet underneath which will be touching the slab. In either case the weight of the granite will not cause a stress crack. Even if you have a sink cutout as long as there is proper support from beneath around the cutout.
Why not do this project yourself? We can talk you through it.

Mark DeFusco