I see it as nearly a double negative. "It's so dark in here that I can hardly see you" means I can nearly not see you. "…I can't hardly see you" then means I am unable to nearly not see you, which to me says I can see you pretty clearly. Not technically a double negative, but close enough that a reversal of meaning can be inferred without much difficulty.

On the other hand, there is no doubt of Huck's meaning, and the usage, however informal, is very common, at least in American English. And it seems to me that in Middle English, and early Modern English, double negative could be used for emphasis of negativity, rather than reversal. Maybe this is a remnant or throwback. Though I never use this construction other than facetiously, I have no problem understanding its meaning.

My hands shook so much I couldn't do nothing with them says "was unable to do nothing," "compelled to do something." No, she would be untied.

Now, "couldn't hardly do nothing…"

Peter