Okay I click "Save as web", I click 60% and save, then "save optimized as" and I want to keep the same file name. Then when I go to close the file it asks me again if I want to save it before closing. I've tried saying yes, and I've tried saying no. Either way I am back to the non-optimized image.
That's the correct behavior. As I explained above, Save for Web is an *export* process. It leaves the original file open and untouched (in terms of modifying the image pixels) other than preserving the Save for Web settings (instructions) with the open file. That's why Photoshop asks if you want to save the original file (to save the Save for Web settings (instructions) with the original file. The reason for this is Save for Web is a 'lossy' process - meaning it degrades the quality of the resulting image.