Funny this would come up today - as I struggled with this for the last 2 nights. I just couldn't get my file smaller than 20kb in PS - no matter what I did (even saving in low res JPEG and cropping the heck out of it!).
Then in deperation I remembered that MS Office suite includes a Picture Manager program. Not very user friendly but , lo and behold, it has a tool where you can shrink an image down to thumbnail for website size!
Took a while to figure how to save the result but once I did that - it was simple to upload a "right-sized" image/file!
If you have MS Office - you're there.