bigger bottle= more water=slower alcohol poisoning of yeast=longer output
Only if you change the concentration of the solution. More water / less sugar.
Say we have two bottles, a 2l bottle and a 4l/1gal jug. Let's compare 3 cases:
A) 2l bottle + 1 cup sugar = x days of CO2 production
B) 4l bottle + 2 cups of sugar = ?
C) 4l bottle + 1 cup sugar = ?
The reason why the yeast stops producing can be either the sugar being totally converted into alcohol, or the alcohol concentration gets too high.
So if you compare case A and B, you start out with the same concentration, and assuming the yeast will multiply over a day or two to a given density, B will output twice the CO2, and you will get to the end of production roughly at the same time. With case C, the sugar may run out before the alcohol level gets too high. But I think at the peak of production, you will still have similar CO2 output for B & C.
Think of it that way - using two separate 2l bottles with a given sugar concentration will give you twice the output, but the same longevity as one 2l bottle. If you combine the contents of these two bottles into one, really you still have exactly the same situation.
Besides this, there are a lot of other factors at play. Temperature being one of them - if you can control that, you can somewhat control the yeast output, although then you got other variables like exact yeast strain etc.
Of course, I could be totally wrong.