Part of the king run, Proverbs 16:10–15.
Quick answer
Wickedness in a king is abhorrent for a structural reason: righteousness is what thrones actually stand on. Power that rots its own foundation does not stay power.
Read both lines
The reason given is engineering, not sentiment: a throne is established by righteousness, legitimacy as the load-bearing element of rule. A king can survive enemies and famine; what he cannot survive indefinitely is the corrosion of the justice that makes people willing to be ruled. Regimes rarely fall the day they become wicked, but the wickedness starts the clock. The verse describes the throne as it ought to work, and the ache it leaves, for a king whose righteousness actually is his throne, does not go unanswered in Scripture (Psalm 89:14).
Related: Proverbs 25:5 · Proverbs 29:14 · Psalm 89:14
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.