It's not just "old money". They own, from what I have seen, the only 2 meaderies in the whole damn province, and mead is something people in Skyrim love. They would have a large and consistent income.
What do they spend it on, though? They have a housemage, which probably is really expensive- especially with the kind of mage they have. They have guards, a lot of them, which patrol the whole of Riften. Those are the only two things I can think of, really, but when you think of how expensive they are, and that the manour (?) is likely Spot Numero Uno for the
then it makes sense. Or not?
Also, I'm sure plenty of Nords can make their own mead. It's not that difficult to do ...
Addendum: As for having nothing to steal ... There's no point in placing valuable loot if there's no challenge in it for the player, is there? May as well throw all that loot in the middle of a road somewhere and have the player acquire it that way.