What you call weight carrying is actual weight distributing hitch. Weight carrying is tongue on ball only.
At 500 pounds dry rating, You'll be over 600 pounds loaded. RVers add stuff. Anything in front of the trailer axles increased tounge weight. No half ton receiver has over 600 pounds of weight carrying capacity. Look for a sticker like this one on the receiver itself. Note the two pairs of weight ratings, 600 and 1000 pounds in my case.

Even if you are under 600 pounds loaded, my opinion is that anything over 400 pounds of TW causes enough weight off the front axle of half tons and smaller to noticeably decrease handling and stability when towing. Think of the truck as a lever, like a teeter tauter. Adding weight behind the rear axle decreases weight on the front axle. Weight on the front axle is important to steering control. So I say use a WDH.
And this is before you add another 300+ pounds in the truck bed. I'm sure you have other camping/riding gear in the bed too. A WDH will also slightly compensate for bed weight too.