And totally missed answering the question- "My basic question is: why do larger tires, (internal volume?), take less tire pressure?"
Contact patch (the part of the tire in contact with the ground)- a 1" square contact patch at 80 psi will support 80 pounds. a 1/2 " contact patch needs 160 psi to support the same weight. Skinnier tires have a smaller contact patch when properly inflated, so they need higher pressure.
(cut me some slack- I had physics, but back when the school computers used punch cards.)