HUCKLEBERRY FINNの話には "let on" が何度も出てきます。 例えば次ぎのシーンです。
"It's all right; I've got it. Take my trunk in your wagon, and let on it's your'n; and you turn back and fool along slow, so as to get to the house about the time you ought to; and I'll go towards town a piece, and take a fresh start, and get there a quarter or a half an hour after you; and you needn't let on to know me at first."
結構難しい単語は知っているのにこう言う簡単な単語を組み合わせた表現は意外と知らないし、普段の生活で英語を使わないので中々覚えられません。 辞書で "let on" を見ます。
・Dictionary.com:
a.to reveal one's true feelings: She was terrified at the prospect, but didn't let on.
b.to pretend: They let on that they didn't care about not being invited, but I could tell that they were hurt.
・American Heritage Dictionary:
a. Reveal one's true feelings or a fact, allow something to be known, as in Don't let on that you met her before. This usage is probably a shortening of let it on someone.
b. Pretend, as in He let on that he was very angry, but in fact he didn't care a bit.
・Merriam-Webster's Online Dictionary:
1 : to make acknowledgment : admit (knows more than he lets on)
2 : to reveal a secret (nobody let on about the surprise party)
3 : pretend (let on to being a stranger)
"let on" には少なくとも三つ "reveal", "admit", "pretend" の意味がありますね。 引用したHUCKLEBERRY FINNの "let on" も最初の方は "pretend" の意味ですが、後の方は "reveal"もしくは "admit" の意味で使っているようです。 この意味での説明は次ぎの辞書の説明がピッタリとおもいます。
・Cambridge Dictionary of American Idioms: to allow other people to know about something He wasn't going to let on that there was any crisis in his family. Usage notes: usually said about something you want to be a secret