what sort of weight can I hang off a drywall screw stud?
How much weight a drywall screw will vary based on a number of different factors including the size and design of the screw and the materials used to make it. These can vary by manufacturer. The type of wood and the type of load are also a factor.
It's possible the manufacturer or your screws has released technical information about the screws you plan to use. Here's an example http://www.trianglefastener.com/pdf/drywall.pdf
Drywall screws are generally not recommended to hold weight such as to hang things off of. They're called drywall screws not hanging-off-of screws. :) They have a thinner shaft and are more brittle than other types of screws.
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)
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.