In their commentary on Proverbs, Bruce K. Waltke and Ivan D. V. De Silva, note that Proverbs 16:31–17:6 form an inclusio (or envelope structure) beginning and ending with descriptions of the glories of old age. I think we may extend that inclusio into a chiasm by including all of 16:28–17:9.
A 16:28 A man of perversities will send forth strife,
And one who bears tales will separate an intimate.
B 16:29 A man of violence will entice his neighbor,
And will cause him to walk in a way not good.
C 16:30 He shuts his eyes to devise perversities.
One who purses his lips brings about evil.
D 16:31 A crown of splendor (is) gray hair.
In the way of righteousness it shall be found.
16:32 Better (is) one slow of anger than a mighty one,
And one who rules his spirit than one who captures a city.
16:33 In the lap will be cast the lot,
And from Yahweh (is) every judgment of it.
17:1 Better a dry morsel and quietness with it
Than a house full of sacrifices of strife.
17:2 An insightful servant will rule over a son who causes shame,
And among brothers will divide an inheritance.
17:3 The crucible is for silver and the furnace for gold,
And Yahweh proves hearts.
17:4 One who causes evil (is) giving heed to lips of iniquity;
A liar (is) giving ear to a tongue of destruction.
17:5 One who mocks the poor will reproach him who makes him;
The joyful at calamity will not be declared innocent.
D 17:6 The crown of the old (is) sons of sons
And the splendor of sons their fathers.
C 17:7 A lip of excellence (is) not becoming to a fool,
Much less to a noble a lip of falsehood.
B 17:8 A stone of grace is a bribe in the eyes of its owner;
Wherever it will turn it will prosper.
A 17:9 The one who covers transgression seeks love,
And the one who repeats a word separates intimates.
The chiasm begins and ends with verses about causing separation between intimates. I have translated the Hebrew as intimates because the word here is not the usual Hebrew word for friend. Within these verses are two (16:29 and 17:8) that do not have specific words in common but do reflect a concern with enticing others into evil ways. The next layer (16:30 and 17:7) is about using lips for good or evil, and within these are the verses about the crown of old age.
Waltke and De Silva describe the middle of the passage, verses 16:32–17:5: The verses within the frame [16:31 and 17:6] largely define righteousness. In 16:31 and 17:1 [should be 16:32–33], God’s rule has priority over human rule; in 17:1–2, spiritual virtue has priority over carnal advantage; in 17:3–5, God’s moral rule has the last word, as seen in his punishment of liars and mockers.
The whole passage is about the effects of righteousness and wickedness in the lives of those who practice them. Strife, alienation of friends, enticement to evil, shame, the judgment of the Lord, reproaching the creator, bribery and other such things result from evil. But righteousness is a crown of splendor. It brings quietness in heart and home, abundance, godly children and grandchildren, and love.