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"Letting on" is "telling everyone." This is significant because the boys believe certain things to be immoral and others to be moral. Huck just wants to get things done; he doesn't care how. Tom likes to indulge in the little white lies and half truths that might mean he'll get into trouble, but because of the way he says things....... they might or might not be true. Tom liked to pretend he was completely principled; Huck was simply Huck.
The Adventures of Huckleberry Finn