Hello, long time lurker, first time poster! In the middle of a master bath remodel and I've a conundrum.

I got some carrara marble pieces fabricated for the shower threshold and pony walls and I got 2-10" and 1-8" corner shelves made as well.
I had a ridiculous experience with our fabricator rescheduling & missing our deadlines, not returning phone calls, etc so when I finally got my lot of pieces 2 months late, I just took whatever they made and ran. They're gorgeous, but the shelves were made 3 cm thick and are HEAVY!
The rest of the shower will be subway tile and I'm worried that when it comes time to install, these babies will be too heavy.
Am I paranoid? Justified? How much weight could subway tiles be expected to hold or is there a better way to support them in install (currently planning on having a handyman set the tile)?
The last thing I want is for these thick shelves to fall down. If they are too thick, what options are available - could a (different!) fabricator cut/grind them thinner?

Please help!