The 2013 Naish pump gauge shows the proper pressure ranges for various kite sizes. Small kites like 7m can be over 8 psi but large ones should have somewhat less pressure. This is because bigger leading edges result in more force on the leading edge fabric and seams...
I don't think that's the reason.
The reason is that a wider diameter tube needs less pressure to be the same rigidity as a smaller diameter tube. There's a fancier way of saying it, but that's what it comes down to.
On average I pump my kites to 10-12 psi in normal conditions. 8-10 psi if it's a particularly hot day. I only use the gauge as a reference, though. I'll give it a ping test and you can also see when the LE fabric JUST starts to swell wider than the seams, it's hard enough. (the stitched seams that wrap around the LE will not expand with pressure, but the areas with no stitching will expand a bit)
It varies from one kite design to another, of course.