Weight distribution

Won't matter as far as payload rating goes, but receivers have a rating with and without a WDH. Without a WDH typically 500 lbs. That's a small trailer but could have a TW of 600-700 lbs? Could tow nicer with a WDH and some weight back onto the steer axle. What are you using for a hitch if you have sway bars?

Pulling with no problem isn’t the issue, while transferring some hitch weight up to the TV’s front wheels and some back to the TT’s wheels with a WDH for better control and braking is the issue. It doesn’t matter what the law is, you need both sway control and weight distribution for safe and pleasant operation.

I don't believe sway control or a WDH is required by law anyplace.
If you don't find the truck being pushed around in your lane, then you probably don't need it with that light of weight.
However, you might find that it does indeed tow a lot nicer with a WDH.