All true, but also be careful of greatly over inflating. If you read the numbers on the side of your tire, they tell you the maximum load for the tire at its maximum pressure. So when does over-inflation start? It is not when you exceed the rated maximum pressure.
Your proper pressure is based on the load actually on the tire now. If you add extra load you need more pressure. But if you are carrying less weight on the tire, it should have lower pressure. You should not have tire maximum pressure with half the weight on the tire.
If you go through the reasoning above, and apply it logically, you would be adding and releasing pressure every time you add weight to the vehicle or take weight off. Nobody is going to do that.
But your car manufacturer also provides upper limits to weight per wheel. You should limit the weight you place on the wheel based on lesser of tire maximum and vehicle maximum. But the pressure in your tires should not exceed that limit expressed as a fraction of maximum pressure.
If you have a tire that says max weight 2000 lbs at max press 40 PSI. That means you should never need more than 20 PSI if the weight on that tire must be less than 1000 pounds based on car manufacturer's advice.
Well, if you are carrying more weight than your car manufacturer advises you must add more tire pressure, another PSI for every 50 pounds of load on the tire. If your tires lose a bit of pressure, add some to compensate.
But if you inflate those tires to 40 PSI when you are carrying only 1000 lbs, your tires will put too small a patch of rubber on the road. You will have the centre of the tire wearing fast, the tire tending to slip sideways on dry road, and to spin on any road. Your braking ability wil be compromised.
Tire manufacturers do evaluate how much of a rubber patch you need for safety.
It is not the minimum possible and it is not too much. The pressure you need is directly proportional to the weight carried to get that rubber patch.
You would get better gas mileage with steel tires on steel rails. But you are not on rails, and you need to retain traction too. You should not try to simulate steel tires on rails by overinflating, ie by incorrectly inflating to maximum rated pressure.
A critical rule is that your car will pull to one side and use a lot of extra fuel if you have a tire on one side harder than on the other. It pulls toward the softer tire. But even worse, when you brake it pulls far too hard toward the softer tire, it puts you into uncontrollable skids.
