Aeropress: does filling it full with water increase the caffeine content of my cup? How does the amount of water I pour into an Aeroporess impact the caffeine content of my cup of coffee? 



If I make two cups, for cup A I use just enough water so that the 1 is covered on the Aeropress, and for cup B  I use enough water so that the whole tube is filled, then what will be the ratio of caffeine in the two cups? Of course, I assume that the same amount of coffee is used for both cups.
Of course, I assume that the same amount of coffee is used for both cups.

In that case:
No
Caffeine dissolves very readily in water. The caffeine content in your cup is mainly and almost solely determined by the amount of coffee you use. The impact of any other factors such as amount of water, water temperature, and pressure are negligible.
To get a rough estimate of the amount of caffeine in your cup do this: multiply the amount of coffee in grams by 10, that's roughly the amount of caffeine in milligrams.