Photodiode + Op-Amp Acting Nonlinearly
The reverse bias voltage across your PD decreases with light and it's not very high to begin with so you're getting less voltage per mW as the light level increases. 

It would be better to use a virtual ground (which requires a regulated negative bias voltage) with an inverting amplifier, in the usual transimpedance amplifier configuration, or to bootstrap a micropower regulator off the PD to give a constant voltage across the PD. The regulator bias current will cause a (probably at least somewhat temperature-dependent) offset, but if the Iq is something like 1uA the (input) offset will be around 1mV.