Banking in the middle ages (which is the basic world in which wizards live) was in its infancy. Its primary reason for existence was to provide safe-keeping, for a price (they took some of your money in exchange for keeping it safe). This could still be the basic mode of banking in the wizarding world, for all we know, which would not encourage people to keep their money in Gringotts (why this is important will be seen at the end).
On the other hand, we can also assume that Gringotts works like a modern bank. It still presents quite a lot of problems: it seems it only has one building (Sirius had to go to Diagon Alley to get money to purchase Harry’s broom), and even assuming it was because his vault was in London, it’s a very ackward situation (and more than a bit dangerous, him being persecuted by justice and all). On the same lines, there is no such thing as an ATM, thus Harry had to take money for the whole year at Hogwarts, and the Weasleys had to go to London to get their money.
Now for the interesting part: wages. There is no indication about how people are paid in the wizarding world, but I’ve lately had the feeling that you’re not paid monthly into your bank account, but (as was the norm in the middle ages), weekly and “on hand”, or even daily.
OK, by now I’ve probably bored you to death with my ramblings, but we’re getting to the explanation. Assuming my bank theory is correct, it can be deduced that most wizard families (especially the ones, like the Weasleys, who live far from their Gringotts vaults) only take their money to the bank when it’s starting to pile up, since it is by no means easy or fast to do it regularly. We know that the money in the Weasleys’ case does not pile up, so they have very little in the bank. The family must save during the whole year to have enough to pay for the students’s materials, and they carry most of that money with them when they go to Diagon Alley. When they arrive, they get whatever is in the vault and put it with the rest they’ve carried from home. So, the Weasleys’ fortune in CS4 is not one galleon and some loose change, it’s quite a bit more, but they just didn’t take it to the bank (because that means driving all the way to London, or using Floo powder which is also expensive), when they can just hide what little Arthur gets from the Ministry of Magic (hopefully someplace safe from the twins).
