Quick answer
Ordinary people can feel who is in charge. The verse measures government by the sound the population makes.
Read both lines
The NKJV footnotes "are in authority" as literally become great, so the picture is of the righteous increasing rather than being installed, which is the same verb chapter 28 closed on when it said the righteous increase. The two chapters are joined at the seam.
What makes the verse useful is its instrument. Not policy, not prosperity, but rejoicing against יֵאָנַח, groaning, the sound of people under weight. That is a test anyone can apply without access to any information a government controls. The book has said it twice already in two chapters, at 28:12 and 28:28, and it will not say it again after this, which suggests the point was considered made.
Related: Proverbs 28:12 · Proverbs 28:28 · Proverbs 11:10 · Proverbs 29:16
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.