Effect of battery size & number?

I've got rather a basic question about the effects of a battery size in LED flashlights..

Besides the increase in max possible brightness , is there any other advantage that larger batteries have over smaller ? I'm thinking here of AAA versus AA/CR123: ignoring the other extra niceties that a larger AA/CR123 flash body might have - clicky, easier to hold etc - is the larger light going to be more efficient for it's weight in any way, or does runtime basically scale linearly with the increase in battery size+weight?

Same question applies to single battery versus multiple - what difference between a single AA/CR123 versus a 2xAA/CR123? Or is it again purely the trade-off of body size + increase in top brightness versus convenience of not carrying extra batteries?

:welcome:
For LEDs it is generally rather different than the old incan flashlights.
In general the only difference a bigger cell makes... say 1 AAA vs 1 AA is runtime. The AA cell has more energy stored within, and it really doesn't affect brightness all that much. (the AAA cell can only give up energy so fast, larger cells can usually give more amps due to lower internal resistance versus a AA cell)
Multiple cells, when we're talking about LEDs generally don't increase brightness either... just give more runtime.

An LED has a certain voltage requirement usualy around 3.5V. Anything less and it just won't light up, much more and it releases some magic smoke. So LED lights are set up to deliver this voltage. WQhat affects brightness in LEDs is the amperage that flows thru the circuit. More amps (generally measured in milli-amps mA for most lights) and the led puts out more light.
So when we add more cells to a light, it just gives higher voltage to the driver circuit to increase (boost) or decreae (buck) the voltage to the proper level... by drawing more or less current from the cell.
Usually a buck circuit will have an easier time supplying ful power to an LED so it is much easier for lights running with more than ~3.5 V to deliver current to the LED.

It's kinda complex if you're new to it, stick around, read up and ask more questions and you;ll get the hang of it eventually.

To answer part of your question: no, it's not a liner scale up. If you keep brightness constant, double the batteries gets you MORE THAN double the runtime. Exactly how much more depends on a lot of different things.

This is a very basic explanation and I may need to be corrected on some points but this is my basic understanding. The voltages of the batteries will affect the brightness of a direct drive light vs a light with regulation circuitry. In similar lights with no regulation a single AA light will be the same brightness as a single AAA light. The difference will be in runtime. Because the AA is larger, it has more mAh (milliAmps per hour) or "juice" than the smaller AAA. With a two AA light, the voltages add up so a two AA light will be brighter than a single AA light in a light with no regulation. If you used the same PR based LED with two AA cells, it will be the same brightness as with two D cells but the two D cells will give you way more runtime because of the larger size. A CR123 cell will provide more brightness than a AA cell because it is twice the voltage. Another factor affecting runtime is the battery chemistry. In a high drain device, lithium batteries and NiMh batteries provide better runtime because they have lower internal resistance. The higher internal resistance in an alkaline battery means some of the energy it provides is lost as heat. Check out the battery forum for a lot of good info.

A Good Place To Start Would Be The Welcome Mat