Quick answer
Different people need different things, and some learn only by watching what happens to somebody else. The verse sorts by teachability, not by worth.
Read both lines
Three characters share the sentence and the correction lands on two of them at different strengths. The scoffer is not the one who learns; the verse does not say he improves at all, and the benefit goes to the simple standing nearby, who takes the lesson secondhand. Then the second line drops the volume entirely. A person with understanding needs only a word, and he gains knowledge rather than merely caution. That descending scale is the point: the more teachable a person is, the less force it takes, and the verse is measuring how much a correction has to cost before it accomplishes anything.
What it does not mean
The verse describes public consequence in an ancient community; it is not an instruction to hit anyone, and it never suggests force produces wisdom, since the scoffer in the line does not become wise. The catalog's standing rule applies here as at 9:8: a verse about a type may never be used to dismiss a person.
Related: Proverbs 21:11 · Proverbs 9:8 · Proverbs 19:29 · Proverbs 17:10
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.