How will a granite countertop on a floating island affect the laminate floor it sits on?
A granite slab of the size you describe and 1 1/4 inches thick would weigh about 300 pounds. A 3/4 inch slab, about 200 pounds.

This is on top of an island that may weigh 100 to 300 pounds, depending on how it is constructed. if you add some contents, the total weight with the thicker granite will probably be between 500 and 700 pounds. If people lean on it, this could add another 50 to 100 pounds of pressure.

The maximum weight of the island, top contents and dynamic pressure is probably about 800 pounds. This is divided over four (or more) support points. Each support is carrying about 200 pounds of weight. This is comparable to a good sized person standing on something the size of the area of the support point. If this were a tiny, sharp metal leg, it might well damage the surface of the floor. If it were a wide 3x6 inch board, the risk would be very small.

Tiny metal glides might do damage. Broad teflon slides, probably not. If you need to use wheels, large diameter rubber ones would probably be fine. Using the thinner granite (if it is well supported and doesn't have a significant overhang) might be better.