The union as in the EU itself? The EU as a whole has definite advantages for weaker members- developmental funding, large free trade bloc and the like- which make staying in it a positive trade off. Or, perhaps, a trade off that is seen as significantly safer/ less risky than the alternative. A proper single economy would have advantages for them too, similar to how somewhere like Alabama in the US is subsidised federally by California's stronger economy; it's the weird hybrid thing that doesn't really work well.
The union as in the monetary union? Arguably, Greece would have been far better off leaving the Euro during its crisis. Instead of having its currency tied to Germany's and effectively having money pumped out they could have set their own exchange rates to improve competitiveness and inflated their debt away at the same time. With a floating independent currency and a weak economy you have a weak currency, and competitiveness improves since you'd get more drachma for the olive oil you sell to Germans and they'd get better value for their holidays so would be more likely to visit. But with a weak economy and a strong currency Middle Eastern or North African olive oil is cheaper, and it's cheaper to holiday in Turkey. It's extremely risky to leave though, and there would be a lot of the more, hmm, strident Europhiles who'd want anyone leaving the Euro out of the EU as well. That's a particular risk for a single, relatively small country like Greece though, not so much if it was the whole PIGS+ since Italy and Spain are too big to kick out.
It's certainly a bad thing if your economy is weak though.
Ultimately the problem is the same as it's been since its inception: the Euro is weaker than it 'should' be for its strong economies, which improves their competitiveness and stronger than it should be for the weaker ones, decreasing their competitiveness. That's a classic viscous* circle for the weak and not really a virtuous one for the strong since the benefit for them lasts only until the time the weaker ones start pulling them down.
*sigh. I knew one of these days I'd actually write it