That's not good. Unfortunately, I don't have any experience with Windows LW: I'm on Macs so it won't work for me. Sorry.
If you did something with WLW yesterday, and have now lost your captions, it sure sounds as if that is the culprit?
Just a wild guess, because everyone seems to be happy with that software, but maybe it does odd things when you edit already published posts? Apparently it works a charm for new posts, but as I said, I have no experience with it.
Your captions are not in your source code, and you have sloppy inserts of the Georgia font spans all over the posts I looked at randomly.
With simple HTML coding, you should be able to assign the font (size, color, family, etc.), with a < div > at the start of each post and close it at the end (< / div > ).
Odd that the captions would continue to appear in your media library, though.
Maybe try with one picture to see what happens if you delete it from a post and then re-insert it to the post. Don't delete it from the media library: if you do, you will have to re-add it to the library and WordPress will add a '1' at the end of the name. Just delete one from a post and try re-inserting it.
Hope someone with WLW experience knows more!