If your tires say max 35 they are likely P passenger car tires. I would recommend upgrading to LT Light Truck tires. They will have a stiffer side wall and perform better towing. Don't ever inflate over the MAX cold tire pressure listed on the side wall. If you got the 35 psi from the door sticker and the tires say 40 or 45 psi or something like that then I would absolutely go to the tire limit if you don't know your axle weights. However:
Tire manufacturer's have load inflation tables. You just use the table to see what inflation pressure you need in the tires to support the weight they are carrying. Most vehicles do NOT need maximum tire pressure to support the actual weight on the tires. Going to MAX pressure "just because" is a great way to make the ride rougher. It could possibly also wear out the center of the tires faster if they are severely over inflated.