Tires & Shocks

Trailer isn't heavy enough for tires to make a difference as long as they're in decent shape. Air em up and go.
Shocks are 8 years old so whether towing or not, shocks may improve handling.
But again, little trailer = not much effect on handling.

New tires and shocks do not increase tow vehicle max towing weight or payload nor do they level the tow vehicle or trailer. Tire weight limits need to be adequate to carry the proposed weight of the tow vehicle and of the trailer. Weighing the tow vehicle and trailer fully loaded is the only way to determine weights accurately. Old tires are dangerous as are under inflated tires. Shocks are partly responsible for stability and ride comfort.

2967 pounds dry? If so, add water, propane, batteries and stuff and you’ll be over 3700.

I don't see much improvement on a rig that light that would not cause more problems.
You could go to LT tires,but I am sure that you are no where near the capacity of the P's that you are probably running now. Lt's would probably harsh your ride for anything other than towing. Some companies do make LT's in a "D" range or one of the new "SUV" tires.
Probably just new shocks would help/
Is their a particular complaint that you have about the performance?

It looks like the 2012 Ridgeline has a strut rear suspension, so it isn’t a matter of simply changing shocks.

A lighter WDH would probably help a lot.

The tires should be ok but if you want to get new ones I would look for the same size and type that came on it. New shocks on the truck would probably help as they are getting a bit long in the tooth.

For a hitch, the Andersen hitch might be a perfect fit. Easy to use and lightweight to move around. Would probably reduce any tendency for the rig to porpoise - especially if the shocks are worn on the truck.
Barney

I haven't really done any significant towing with it yet. Also it indicated I got for relies but could only view one. Vincent

Jack1776 wrote:
I haven't really done any significant towing with it yet. Also it indicated I got for relies but could only view one. Vincent

If you are talking about the replies here, try doing a refresh on your computer screen. Or you could jump to a different forum then come back.
Barney

If your trailer is within Honda specs as outlined in your owner manual for weight, hitch weight, and total frontal area try towing it without changing anything first.

Vincent, one other thing. The 2967# seems very specific. Is this the dry weight? You will want to base any decisions on the gross weight of the trailer, or at least the max weight you will have if not gross.