Quick answer
Two of the heaviest things a person could be asked to carry, and the verse says a fool's anger outweighs them.
Read both lines
The comparison is chosen for a specific quality rather than raw mass. A stone is heavy but you can put it down. Sand is worse, because it shifts, cannot be gripped, and gets into everything, and a load of it does not distribute. Then the second line says the fool's wrath is heavier than both, which is a claim about what it is like to be near it rather than about its physics.
What makes it heavier is left for the reader, and the chapter has already suggested it. Sand has no shape; a fool's anger has no proportion and no end point you could work toward. A reasonable man's anger tells you what to fix. This does not, which is why it cannot be set down.
Related: Proverbs 17:12 · Proverbs 12:16 · Proverbs 29:11 · Proverbs 27:22
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.