I just finished checking RAM use by galaxy size and here are my results. The figures are all total amounts. All figures in the first table are just to the first turn. Each time, I exited the game and restarted it.
Idle OS + steam + all the monitors I have running
GC3 Start menu 3.69 GB -- added about 1.3 GB
GC3 Tiny galaxy 4.49 GB -- added about 0.8 GB
GC3 Small 4.53 GB -- another .04 over Tiny
GC3 Medium 4.56 GB -- another .03 over Small
GC3 Large 4.71 GB -- another .15 over Medium
GC3 Huge 4.92 GB -- another .21 over Large
GC3 Gigantic 5.28 GB -- another .36 over Huge
GC3 Immense 5.92 GB -- another .64 over Gigantic
Then I exited the game and reloaded a game I had in progress at turn 54 with what looks to me like about 15% of the galaxy explored, all opposing civs selected, all game variables at maximum ("star frequency = abundant", "planet frequency = abundant", etc), 16 colonies, 30 ships, 8 star bases and one shipyard, no mines, rally points, research just barely into the "age of war", and about a dozen custom ship designs.
GC3 Immense reload 6.06 GB -- another .14 over Immense turn 1.
All of these figures are for this one time. I have seen variances before when I have ran this sequence repeatedly, so as they say, your mileage may vary. I have seen it go as high as 7.6 GB when playing an immense galaxy.