No, you do not need it, but it sure makes towing nice. If you are just towing around your area then don't bother with the effort to hook it up, but if towing long distances then the little things will make it more enjoyable. The WDH will level out the truck so it does not sag and your headlights do not point up off the road. The WDH itself might oferr some sway control on a small trailer just due to the added friction, but unless you trailer sways then i would not worry so much about it. loading the weight on the trailer axles or just forward of it helps to minimize sway. Putting too much weight behind the axle will make it sway.
I had an 800lb (so the manufacturer claimed) cargo trailer and IDT it was too heavy loaded, and always used WDH, even when I had a 3/4 ton truck. It just kept everything happy.
I even had trailer brakes because I would go through, and down, mountains and having trailer brakes is more relaxing. The truck stops itself and the trailer stops itself so there is zero added weight to your truck's brakes.
If you have a WDH then use it, but the added cost, $250 plus, might not make it worth getting.
As I said, dont bother with one for short in-town trips.