First things first, you are NOT illegal except in certain provinces in Canada where GVWR is law, and they do weigh RVs. I think British Columbia is one of those place.
What were you supposed to do beforehand? Yes, take it to a scale and get it weighed. Obviously that is almost never a practical suggestion. What you REALLY needed to do was go into the whole deal with a little better understanding of the reality of camper weights and truck payloads. You may not have gone with this particular combination if you had realized how heavy it was.
What do you do now? Well, you can put a for sale sign on the camper and look for something lighter. You can put a for sale sign on the truck and try to find something heavier. You can throw caution to the wind and hit the road.
Since you've already hauled it you know how it handles to a degree. If you're happy with it, then make sure your maintenance is up to date, make sure your insurance premiums are paid up, and go camping.
You might consider some suspension upgrades to the truck if you don't already have them, as tires are only part of the puzzle. Options here include airbags, helper springs, or reworking the factory spring pack to eliminate any rear end sag you might be experiencing. The truck handles better when it sets level. Better shocks and a heavier sway bar will help with cornering and lane changes on the highway.