Not sure what you mean by "weight limit" - the reason why the mass of bismuth shouldn't matter as far as distances are concerned is the same reason why mass doesn't matter when you're calculating the acceleration due to gravity: the diamagnetic force exerted on the bismuth will go up or down in proportion to the mass of your sample.

Now, if you are using an electromagnet, then the interaction of the magnetic field of the object being magnetized (or diamagnetized) exerts an inverted electrical potential in the circuit generating the magnetic field in the first place, thereby weakening the magnetic field and creating a limit to how much force is generated by the magnet. I don't know what happens if you have a static magnetic dipole like a ferromagnet interacting with another magnetic field; there must be some kind of counteraction, but I just don't understand ferromagnetism well enough to even say what the mechanism would be, let alone how to calculate it.

If you have an electromagnet, then your electromagnet is probably rated for a certain amount of force - apply too much, and you will break it. All you need to do then is calculate the force that you want to apply to the bismuth, and make sure that is within the capacity of your magnet. If you are using a ferromagnet, or if your electromagnet is not rated, then I cannot help you.