The shot load is an important factor in required strength of the gun. Shooting purpose and shot charge weight are joined at the hip. The 1 1/4 oz proof is for pigeon/duck/high phez guns, where as 1 1/8 oz is for game guns (we'd call them upland bird guns) and the 1 1/2 oz is for fowlers.
Pressure is not defined by shot charge weight; influenced, but not defined. Note that CIP (European) pressures are standardized at lower values than are SAAMI (USA) standards.
A light shot charge in a high pressure loading can be damaging/cyclic life shortening to heavy proofed gun's actioning. Likewise, a heavy shot charge low pressure load can be damaging to the wood of a lighter gun. Match pressure to the metal and recoil to the wood.
For older doubles, think in terms of light shot charges (3/4 - 1 oz), low pressures (5000 - 7500 psi), low velocities (1050 - 1200 fps), and a service/repairs warchest.
