Is the weakness also doubled on a critical hit? For instance, mummies have weakness 10 to fire. Is weakness also doubled and thus the mummies suffers 20 damage from fireattacks instead of 10 on a normal fire based attack?
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The only "external" damage that gets doubled (see page 308 sidebar on Critical Hit Damage) is conditional & circumstance bonuses. I'm pretty sure the extra damage from weakness is not considered either of those, so no, it doesn't double. But hey, neither do resistances.
The definition of Weakness on pg 294 implies that Weakness becomes part of the base damage. That, combined with the explicit mention that you double anything that isn't critical-only from pg 308, makes me think you should double weakness. And probably Resistances as well.
I feel like the answer is probably no.