Sam, a 6S 2500mAh pack would be the same weight as a 3S 5000mAh pack - look at the power of the battery - 22.2x2.5 = 55.5Wh, 11.1x5 = 55.5Wh. What affects the weight of the battery (essentially) is this power rating.
Basically, it is as Chris_Dono and Sam (BRS) have said, it's to do with efficiency. 2000KV geared up will do all the things that 2200KV will do, but will take a little more power to do so. Therefore, the overall efficiency is lower.
Gearing up/down is of course the cheapest way of doing things, and with the big motors, they're not particularly fussy, unlike 1/10th motors, so the differences aren't that much.
The ultimate efficiency run is to go as high voltage as possible, retaining the same total power. This is why the national grid is at such high voltage - the current is met with resistance, causing heat build up. That heat build up is where electrical energy is transferred into heat energy - thus less efficiency, as energy is lost from the intended purpose. The higher voltage you have, the less current you have for the same power output, and therefore, the higher efficiency you have.
Gearing a motor up draws more current, whilst when using a higher KV to do the same thing, the amount of additional current required is lower.
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