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Its not his weak spot you can still penetrate other spots of his hide with black arrows but that spot was penetrated by a black arrow and woulfnt it be better to hit the spot already weakened than shoot 2 arrows in the same spot or riddle him with arrows plus alduin can only be killed by the dragonborn
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Well that was his weakest spot. And screw dragonborn if a human can kill alduin smaug can.