Trailer weight will determine whether it has a single axle or dual axles, usually. The cross-over will be in the 3500-4000 GVWR range, because the heaviest axles popularly used for light trailers are rated near 3500. From there they go tandem, can take up to 7500 before a stronger axle is needed.
Weight distributingis not a function of the receiver on your truck, it is a function of the type of hitch you install. Pretty much all Class III and heavier receivers installed on trucks and SUVs are designed to be used with a WD hitch. Class II, maybe, maybe not. They do make low capacity WD hitches with the small shank for a Class Ii, but you need to be sure the receiver you have is rated for what you will tow, weight distribution or not.