The honey returns from verse 16, and the second line is the hardest sentence in the chapter to translate.
Quick answer
Too much of a sweet thing is bad for you, and chasing your own reputation works the same way. The comparison is clear even where the Hebrew is not.
Read both lines
The first line is verse 16 restated flatly, without the question or the vomiting, which suggests the chapter is deliberately closing a loop it opened eleven verses earlier.
The second line is where translators work hardest. The Hebrew reads, closely, "and the searching out of their glory is glory," with no negative particle of its own, so the NKJV carries the "not good" forward from the first line to produce "to seek one's own glory is not glory." Other versions handle it differently. This expression is debated, and the entry rests only on what the parallel structure requires: whatever the second line says exactly, it is the honey warning applied to self-promotion.
One thing the Hebrew does make visible is a bracket. The word for searching out is חֵקֶר, the same root as verses 2 and 3, where searching out a matter was a king's glory and a king's own heart was unsearchable. The chapter opened by praising investigation and closes by warning about one particular subject of it, which is yourself.
Related: Proverbs 25:16 · Proverbs 25:2 · Proverbs 27:2 · Proverbs 25:6–7
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.