How much weigh can a torque carry?
The rating is magnitude of the torque, which is simply the scalar magnitude of the vector cross product between force vector F  and the lever arm displacement vector r. The units are force * distance (coincidentally the same as the units of work) and usually datasheets use mass units rather than force, so the force a certain mass experiences under 1G gravity. 



In the case where the force is perpendicular to the lever arm and to the axis of rotation you can simply multiply the scalars. In other cases, the force will be transferred through the bearing or whatever is constraining the motion to be rotation about the axis. 

In the example from Wikipedia shown above, if we visualize the earths gravity as being  in the z axis, the weight the motor can drive is essentially unlimited if the rotation axis is vertical. That's because the motor need only provide the torque to accelerate the mass, and that can take place slowly for bigger masses. 

If the rotational axis is horizontal with the lever arm perpendicular, then the maximum torque is when the lever arm is horizontal, and the magnitude is the length of the lever arm (say 1cm) multiplied by the force (that experienced by 1kg or about 9.8N). 

The same torque can be created by 100g at 10cm or 10g at 1m. 

If an equal lever-arm-times-mass was horizontally opposed (statically balanced) then there would be no hard limit to the mass, just as in the first case (at some point the friction in the bearings would cause problems). 

It's like tightening or loosening a nut with a socket as shown on this page: 
 

The torque experienced by the nut is the cross product between the force applied to the ratchet handle and the lever arm. A longer lever arm means more torque for the same force.