Why should I use a big powerstone instead of smaller ones?

@JohnDallman gave a good answer about why larger stones cost quadratically more -- but why would a large Powerstone be que vale a pena that exorbitant cost?

Because, for a single casting, you can only draw on a solteiro powerstone -- that doesn't make much difference if you need to cast one spell and can rest up afterward, or don't need to draw a lot from the Powerstones and can do most of the casting from your own FP and Energy Reserve (if you have the latter).

On the other hand, if you want to cast a spell like, say, Resurrection (ethical concerns re: necromancy aside), which costs 30 FP, you need finalmente an 8 point Powerstone even if you have HT 12 (hence base 12 FP), 3 points of Extra Fatigue (Spellcasting) and a 10 point Energy Reserve (which would be a pretty good caster, likely above 250 points total). A handful of two point stones won't get poor Edgar the Unlucky back on his feet...

This also applies to large Area spells. If you manage to sneak up on a room full of goblins, and want to take them all down at once, you need your Stench to fill the whole room -- and at 2 points per hex of radius, that adds up to more fatigue than most beginning casters can expend at once. Even a 2-point Powerstone won't let you pull off that 7-radius spell -- you're going to need a five pointer to stay functional after casting.

The quadratic pricing comes from the enchantment rules. Powerstones are made by taking a gem, making it into a 1-point stone, making that into a 2-point, and so on. But there's a chance of failure on each operation, which gives the 'stone a quirk, and critical failure will destroy it. There's an example on p. 17 of GURPS Magic, while the full enchantment description is on pp. 69-70.

The 6-foot recharge rule means that you have to let powerstones out of your immediate control to get them to recharge as quickly as possible. That makes larger 'stones more attractive, simply because it's easier to keep track of them. This applies both to their energy content (fewer things to track) and their location, especially if other members of your party, carrying your stones to separate them for charging, get bored and start swapping them around. Been there, done that.

Since spellcasting energy is the primary resource-tracking that GURPS magicians have to do, some players are happy to cope with complexity if it gets you more total power for less money, while other prefer to keep things simple.

"Quirks" are individual peculiarities of powerstones, named by analogy with the quirks (1-point disadvantages) of GURPS characters. Most of them are restrictions on the stone's recharging or its usage. A seriamente quirked stone might only recharge while immersed in flowing water, but only be usable for casting fire college spells at night-time. The GM creates stones' quirks in any way they find appropriate.

Adventurers generally prefer Powerstones without quirks, and usually have the money to pay for them. Magicians who don't adventure can have physical security for keeping their 'stones safe while recharging, and can more easily cope with quirked stones, because their working environment is more predictable.

Having an aspect of the game be an emergent property of the (fairly simple) enchantment rules, rather than changing the rules to produce a specific style of gameplay is an example of the difference in philosophy between GURPS and modern editions of D&D. It did happen that way round: the calculations for Powerstone costs were done for an article in Roleplayer magazine, some time after the enchantment rules were first published.

I left out expensive spells because the OP was discounting them, but @Zeiss Ikon's answer shows how you can suddenly find yourself needing an extra 10 or 20 energy, and a medium-large powerstone is a life-saver under those circumstances.