First off, you do not have too much trailer for the truck. That truck will tow your trailer and larger ones if you decide to upgrade later.
Yes, you should have a weight distribution hitch. They've available on Amazon (free delivery) for a reasonable amount of money.
Here's a reasonable $180 option.Do you have load range E tires on your truck, if not get some.
It sounds like you need a better brake controller that's adjustable. Again on Amazon, there a lot of them. Most of them are plug-n-play whereas you just plug them into the trucks wiring harness though they may not be available for an older truck.
What I'd do, is take the trailer and truck to an RV dealer and have them install a good brake controller, check/grease the wheel bearings adjust the trailer brakes (could need new brake shoes) and then make sure the newly installed brake controller plays well with the trailer brakes.
Then install the new WD hitch you bought and see how it all works from there. You make have to make adjustments, but yo need to take care of these basics.
If the electrical plug in on the truck or the trailer need to be replaced, the RV repair shop can do that also relatively cheaply.
Bill