Why do you think the lords of the Vale arte so poor?!

I think there’s a couple reasons:

1. there’s a sharp division between the lords of the Vale proper and the lords of the Fingers and the islands. The former have all the rich farmland and arable land of the valley, whereas the latter have less and poorer soil that’s much more mountainous. So there’s a lot of inequality within the nobility: consider the difference between Petyr Baelish’s father and the Royces of Runestone, for example.
2. the lords of the Vale are traditionalists, even more than most. They don’t act in a profit-maximizing fashion, they concentrate on agriculture rather than trade (hence why Gulltown is so small), and they would never think of economic development (hence why the mineral resources of the mountains haven’t been tapped into as in the Westerlands).   
3. when you get down to it, the Vale is not that big. It’s quite fertile, but it’s not as big as the Reach and it’s not going to grow any time soon. This means that the Vale can’t expand its economy easily just by bringing new land under the plow (because all the land that can be grown on already has been) or by increasing the number of hands in a field (because that threatens overpopulation).