How to install wheels on shelves

Anchoring them to studs is just fine, your main problem is going to be getting brackets that will support that amount of weight. The amount of weight each bracket will support will be printed on the package. I would consult your granite or stone supplier for weights of their products.

You MUST make sure that you're anchored into studs, though, and preferably with three inch wood screws that are NOT drywall screws.

It sounds like you have a floating shelf. Because of the shear forces, these don't hold very much as they just end up pulling away from the wall.

If you want to pile heavy books on it, you are going to need to support it properly. The words "decorative" and "strength" don't usually go well together. I would think you need something solid and not a rope. With rope you have to worry about tensile strength, stretch and how to anchor it (will the anchor now hold the weight?).

The best thing to do is install a bracket below the shelf to support it. How many of these you need will depend on how long your shelf is and what it's made out of. You could always start with two (one on either end), and if the shelf is sagging, install another one in the center. There are "decorative" brackets out there but the basic principal is the same. Make sure you anchor these into a stud and not just the drywall or else you'll end up just pulling the drywall off your wall.