In Photoshop (At least the version I am using) go to the "File" menu and then Export, and select "Save for web (Legacy)" and it will pull up another window where you can select jpg, and a quality level and change the image dimensions to something smaller, it previews the expected file size so you can fiddle around until you get to the 200KB mark. I have found that much better for trying to squeeze something that looks OK at a reasonable size in to the 200KB limit than trying to resize it manually.
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