Would this product mess up the floor underneath the mats? With the pressure/weight of the equipment on top of the mat, would this cause any damage to the floor over time?

Our 8mm Strong Rubber Rolls won't damage any subfloor. Rubber is meant as a layer of protection over any subfloor, whether it be concrete or an existing flooring surface. Depending on the flooring surface under the rolls, we may recommend placing a plastic sheet under them to prevent staining. Examples would be light colored carpets, standard vinyl floors, and some hardwoods.