The limit on the stepper motor is the torque it can produce. This has nothing to do with the weight it is rotating, except that the weight may cause more friction, which the motor has to overcome.
The mass does matter somewhat, but only in a rotational sense, and only to determine how fast the motor's torque will speed up the rotation. The proper term for this "rotational mass" is moment of inertia. The torque divided by the moment of inertia about the rotating axis gives you the angular acceleration.
Another limit is what the motor bearings can handle. The motor datasheet should give you the maximum axial and radial forces the motor is rated for. In your case, the axial force is the weight of the platform and everything on it, minus the weight taken up by the wheels. That may be hard to determine, since it's not clear how much of the weight is supported by the wheels and how much by the motor shaft.
In the end in this case, the limiting factors will be the friction and therefore the torque required just to get the platform rotating at all, and how fast you want to get it up to speed. The former depends on too many things that are hard to know up front. Build it and see, then get a motor with enough torque to reliably overcome the friction.
You could also use gears or a belt drive to effectively turn a fast but low-torque motor into a slow but high-torque motor.