Is pressure regulator size directly proportional to inlet or outlet pressure? In other words, will the size of the pressure regulator get bigger if the inlet pressure is higher?
The size of a pressure regulator is generally related to differential pressure (defined as P1 inlet - P2 outlet in absolute values) and max flowrate. There are two conditions that you need to take into consideration, Sub-critical drop when P2>P1/2 and Critical drop P2<=P1/2 (always consider absolute pressures), in the first case the sizing is mainly influenced by P1-P2, in the second P1 is dominant. Nevertheless, depending on the application, there are other factors which must be considered for a proper sizing: orifice size, min flowrate, noise level, accuracy and other requirements which can influence the size choice.
In general, Inlet pressure increase will typically reduce the size of the regulator.