Quick answer
Money feels like insight from the inside. The verse says a poor man with judgment can see straight through him.
Read both lines
בְּעֵינָיו, in his own eyes, is the phrase chapter 26 used three times for the man past helping, and here it is attached to wealth specifically. The mechanism is easy to recognize: success in one area gets experienced as competence in general, and nobody around a rich man is positioned to tell him otherwise.
The second line supplies the person who can. The verb is יַחְקְרֶנּוּ, searches him out, the investigating word chapter 25 used of a king's glory, and the one doing it has no standing and no leverage. That is the verse's quiet reversal: the man with the least reason to be listened to is the one who has him accurately assessed, and the assessment costs the rich man nothing precisely because nobody will hear it.
Related: Proverbs 26:12 · Proverbs 26:16 · Proverbs 18:11 · Proverbs 28:6
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.