⚑ The chapter's pastoral centre, and one of the clearest verses in Proverbs on how to be near a suffering person.
Quick answer
Cheerfulness aimed at someone in grief does harm, not good. The verse compares it to stripping a coat off a cold man, which is how badly it misses.
Read both lines
Three images and the first is the one that stays with you. Taking a garment away in cold weather is not a failure to help; it is an active removal of the little warmth the person had. So the saying is not describing a well-meant gesture that falls flat. It is describing something that makes the situation worse, delivered by someone who thought they were helping.
The second image is chemical and probably reactive, vinegar poured on soda, which fizzes and destroys both. The third names the behavior plainly: singing songs עַל לֶב־רָע, over a heavy heart. Note that the singer is not malicious anywhere in this verse. He is cheerful, and cheerfulness is the problem, because it requires the sufferer to either perform a mood he does not have or explain why he cannot.
What it does not mean
This is not an instruction to leave grieving people alone, and it is not permission to avoid them because you might say the wrong thing. What the verse forbids is a specific move: applying brightness to a heaviness it has not acknowledged. It says nothing against presence, and Scripture's clearest picture of doing this well is Job's friends before they opened their mouths, sitting on the ground with him seven days and nights, saying nothing, because they saw his grief was very great (Job 2:13).
The New Testament gives the positive form directly: "Rejoice with those who rejoice, and weep with those who weep" (Romans 12:15). That is the route this catalog takes for wounded verses, and it is deliberately not the passage most often used to hurry a suffering person past what they are actually in. Ecclesiastes says there is a time to weep and a time to laugh (3:4), and the whole skill this verse is asking for is knowing which one somebody is in. It is also worth saying plainly that depression and grief can be medical, that a song will not touch either, and that no proverb overrules getting a person real help.
Related: Romans 12:15 · Job 2:11–13 · Proverbs 12:25 · Ecclesiastes 3:4 · Proverbs 25:11
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.