ok. I'm not a tire expert but this is the way it breaks down in my head. If somebody with more expertise sees something wrong with this thought process, please speak up.
So let's say we have a 4000 pound Jeep with perfect weight distribution...1000lb/corner, and a certain area (the contact patch) of the tire in contact with the ground. In that contact patch and based on the first law of physics, you have 1000 pounds pushing up on the outside of the tire and 1000 pounds pushing down on the inside of the tire (we'll neglect the support provided by the sidewalls since it's really not significant as can be seen by how flatly it squishes when the tire is flat).
So that 1000lb pushing down on the inside of the tire is air pressure spread out over the area of the contact patch. So the higher the pressure, the smaller the contact patch and vice versa.
Now where size comes in, is that size of the tire does not change this. So a 35x12.5 at 30 psi is going to have the same contact patch as a 30x9.5 at 30 psi. The problem is that the size of contact patch for one is not appropriate for the other. To make the 35 have the same contact patch as the 30 means it's underloaded/overinflated, riding hard, not wearing evenly and probably helping your gas mileage by an amount that matters to the EPA but a real human will never notice. To make the 30 have the same contact patch as the 35 means it's overloaded/underinflated, riding way too comfortably

, wearing unevenly and to the extreme may overheat and blow out on the interstate.
To into examples, let's take two pairs of tires of the same model where one has the width as the variable and one has the diameter.
BFG KO2
31x10.5R15 2270@50psi
33x10.5R15 2600@50psi
33x12.5R15 2205@35psi
35x12.5R15 2535@35psi
The fact that in each case, the larger tire has a larger load rating at the same pressure demonstrates that the larger tire is intended to have a larger contact patch, and to maintain the appropriate contact patch for the tire at the same load, the larger tire would take a lower pressure.