Quick answer
The oppressor here is himself poor, and that is the whole point. The verse is about harm coming from the direction it was least expected.
Read both lines
Everything turns on who the subject is. This is not a rich man grinding the poor, which is the book's usual target and which it condemns repeatedly. It is גֶּבֶר רָשׁ, a poor man, doing it to דַּלִּים, the poor, and the shock of that is deliberate.
The image explains why it is worse rather than merely sad. A driving rain should be the thing that grows the crop; instead it beats it flat, and the NKJV footnotes the second line as literally and there is no bread. So the harm comes from the quarter that was supposed to bring relief, which is exactly what a poor man oppressing his neighbors does to a community that had nowhere else to look. The verse belongs to the poverty-and-injustice thread whose home entry is 13:23, and it adds something that thread needs: oppression is not only a thing the powerful do.
Related: Proverbs 13:23 · Proverbs 22:16 · Proverbs 14:31 · Proverbs 28:15
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.