I need help finding quotes that would show Huck's gradual progression throughout the story.
A prime example can be found in Chapter Sixteen and reflects Huck's increasing moral maturity. He muses: "Conscience says to me 'What had poor Miss Watson done to you, that you could see her nigger go off right under your eyes and never say one single word? What did that poor old woman do to you, that you could treat her so mean?...' I got to feeling so mean and so miserable I most wished I was dead." This shows Huck's burgeoning conscience.
A second example comes from Chapter 19, when Huck comes to the understand true nature of the "king" and the "duke." He says, "These liars warn't no kings nor dukes, at all, but just low-down humbugs and frauds." The idea will help Huck mature and be more wary of such unsubstatiated claims in the future.
A third example can be found in Chapter 40. Though he still has some growing to do in terms of morals, Huck is finally beginning to discard the prejudices with which he has grown up. When Jim is hurt, Huck decides, "I knowed he was white inside, and I reckoned he'd say what he did say - so it was all right, now, and I told Tom I was agoing for a doctor."