It is an abomination to kings to do evil, for the throne is established by righteousness.
Proverbs 16:12 ESV
This is the inverse of v10. A king who does evil is an abomination to God. If he wants his rule to be firmly established and his house to carry on, then he will rule according to God's Law.
A just balance and scales are the LORD's; all the weights in the bag are his work.
Proverbs 16:11 ESV
Like a king whose heart is right with God, a just balance and scales are an instrument of God's will. I think this is deliberately placed in parallel with v10, so that the just weights in the bag and the king who judges according to God's Law are both instruments of God's will.
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