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It's good to remember that jpg is lossy. This means that it says to itself: "Ahh, those pixels are nearly the same. I'll just remember one value for all, and that will have to do. No one will notice."

This is handy, and even necessary because otherwise the filesize would be too big for the Internet.

jpg is great with photographs of skies etc, but the more changing colours it encounters, the less it can compress. The same goes for sharpening. The final work can indeed be sharpened, but personally, I wouldn't sharpen a thumbnail too much as it does increase the filesize.

Just try this out, and exaggerate: open a very coloured photograph with some rather shart edged objects and save it  AS A COPY (can be set in the opening dialog box. this means that the original is kept open. If you don't do this, it will be the jpg you will have open) as a jpg (save for web). Write down the filesize at a certain quality setting of the slider. Now go to Filter menu, open Sharpen, Unsharp mask and set the top slider so that the image becomes very blurry. You may really exaggerate. Save again as a copy with the same quality setting. Now compare the file sizes.