If a character has a specific weakness, this can be represented as a power fact as well. Enemies who introduce a source of weakness can use it to compel the character's power-related aspect(s).
For example, a vampire might have a power fact that reads "Unable to face holy symbols". When confronted by a master vampire hunter, the vampire might be offered a Compel: "Because you are a Bloodsucking Master Vampire, the holy symbol drives you away and allows the hunter to save your latest victim. Damn your luck." Even if the vampire refuses that compel, the power fact is still true, and the vampire does not have narrative permission to face a holy symbol or its wielder. He must work around the hunter in some way, perhaps by attacking a different target, causing a distraction, or having his mesmerized victim attack the hunter by surprise.