What is the maximum weight loading from a drywall screw stud?
First there is no easy way to answer the question.  It is a physics question that requires:


length of area of screw inserted into framing
the ability of framing to hold screw (this would involve a very complex set of equations)
angle of the screw
materials and manufacturing process of the screw (even with drywall screws there is a spectrum of quality)
temperature (not a huge factor but still)
the verticality of the load
time (the ability to hold an object will dissipate as screw becomes loose when loads get to more than 1/3 to 1/2 of its capacity)


Here are some numbers for wood screws into 2x4 framing.

Just to give a round number I would be comfortable saying 100lbs for a drywall screw drilled 1.5 inches into a premium southern pine 2x4.  Just into drywall... 2lbs.