Why? (Beyond transactions costs associated with using exchange rate markets.)
It is one thing to say, "people don't have confidence in the dollar, and therefore an exchange in euros will atract more users;" and another thing to say, "because a anti-US regime insists on (subsidizes?) an exchange that officially quotes prices in euros, therefore people will lose confidence in the dollar."
Anyway, rather than strong versus weak, I think the better way of classifying currencies is hard versus soft. Iran can subsidize every barrel exchanged on its bourse and we'd see large volumes trade, but it would not mean much at all. (The ease-of-transactions premium on dollars is not zero, but I would have to see some evidence that it is econometrically detectable.)
Why?
Because nations could now buy oil with Euros and this would free them from having to have only dollar cash reserves for purchasing oil. Currently all oil is purchased with dollars which keeps the dollar in high demand around the world.
Theoretically, with oil-for-Euros the dollar demand drops.