Size matters, well, at least some time ago it did. I remember that I worked up the standing ladder for Core Complexion (Corp Size = Huge) and Roden Shipyards (Corp Size = Medium) many years ago, and it went much faster to gain high standing for Roden Shipyards. The smaller the NPC corp the faster you gain standing.
A concrete formula for Corp Standing increase is here:
Corp standing increase
= Agent standing increase * Agent efficiency / Corp size
Agent efficiency
= 0.01 * ((8 * Agent level) + (0.1 * Agent quality) - 4)
An estimated empirical range of values for the Corp size factor is here:
Huge : 0.8 - 1.0(?)
Large : 0.6 - 0.7
Medium : 0.4 - 0.5
Small : 0.2(?) - 0.3(?)
Tiny : 0.1(?)
Both quotes are from 2010 and I don’t know if this formula and the values are still valid today. Certainly Agent quality doesn’t exist anymore but the formula might still hold with a constant value for this parameter (maybe 20 (?), which was the old highest Agent quality, or 0 (?), which was the average (Agent quality could range between -20 and 20 back then)).