How much weight will a 2x4 stud hold?

Using a syp (southern yellow pine) stud in a compression lift will handle 3000 lbs before it begins to bow. A stud used in a shear panel or with a strong back carries a load well above any residential application. I replace structural columns with syp studs in a vertical lift. Always inspect the lumber. Excessive knots or torsional twisting of the lumber is unacceptable.

Well, as a stud it is functioning in compression. Assuming you put in enough blocking to prevent if from bowing under load, a single stud can support thousands of pounds. It really depends upon the species of wood, however, if you you want an exact figure. Let's just say that it is in the neighborhood of about 10,000 pounds. Way more than any stud in a home takes. But if you don't install blocking and the thing bows under pressure, it can support much less. Maybe a couple of thousand pounds.

Is this a treated or untreated 2 X 4?

over what span?