How much weight can a motor take before it can't run?
The data is all given on the page you linked.



The relevant quantity is the "Stall Torque", which is the maximum torque the motor is able to exert. Note - as the warning text, below the table, says, you should not plan to operate at this stall torque for more than a few seconds at a time.

To convert stall torque to "a weight", take the stall torque in ounce-inches and divide by the radius of your wheel, in inches. The result will be a number of ounces, representing the maximum weight the motor can hold against gravity.





However you are probably more interested in moving a robot around a horizontal surface on wheels. (Your question only mentions "a weight" which is vague.)



Let's suppose we have a robot with a single driving wheel, as shown above. It is driving around on a perfectly level surface. Since the ground is flat, gravity does not affect the robot (except to keep it pinned to the ground) so the robot does not require any torque to stay still.

Assuming frictionless bearings, any motor will be able to move the robot. The more powerful the motor, the faster the robot will accelerate.

The acceleration of the robot is given by combining:

$$ Force (N) = Mass (kg) \times Acceleration (m/s²) $$

and

$$ Torque (N.m) = Force (N) \times Wheel radius (m) $$

Suppose we have a car that weighs 500 kg, with a motor exerting 5,000 N.m of torque on a driving wheel with radius 0.5 m.

The force (N) exerted by the wheel is 5,000 N.m / 0.5m = 1,000 N. The acceleration (m/s²) is 1,000 N / 500 kg = 2 m/s².

Note that there is no single "maximum weight". These equations say that no matter how weak the motor, you will be able to move the car. However a small motor won't accelerate the car very fast, or be able to drive the car up a hill, or be able to overcome the friction of the bearings and air drag. You have to decide what your criteria are for these parameters, which will determine the maximum weight of your robot, for a given drive torque.