Why does the gain of a RC filter vary with input amplitude in LTspice?
The "gain" you see in the plot is always referenced to an AC amplitude of 1. Since you're changing the amplitude, it's not strange that the amplitude shown is different. This becomes more obvious if you open up the settings for the plot window and select Linear instead of Decibel.



Try measuring directly on the output of the AC source - it will show the same magnitudes as you see for 1 Hz in your filter.

Remember that the AC simulation mode is a bit special, in that it is doing a "small signal analysis". You won't get effects from non-linearities such as clipping due to excessive voltages.