browser extension to replace JavaScript file on a live site for testing

Alternatives:

• Using chrome you can change code on the fly (Developer tools -> Sources tab) and just save it (command + s)
• Use the LiveReload app that actually attaches an extension (that kind of does what you want) http://livereload.com/

This may not be the "exact" answer to your question, yet I almost sure one of those will do what you want to do.

The Opera browser has similar functionality:

1. View source code of the page (Ctrl+U).
2. Make some changes. Or paste and replace the entire file.
3. Press Apply Changes in the toolbar (Ctrl+R).

For editing linked resources (such as javascript or CSS files), use the following approach:

1. Open the linked resource in a new tab.
2. View "source code" of the resource (Ctrl+U).
3. Make some changes.
4. Press Apply Changes in the toolbar (Ctrl+R).
5. Return to the tab with the webpage and realod (Ctrl+R).

Try http://www.fiddler2.com/fiddler2/version.asp

It does that and much more. But it's not a browser extension.

I think this is a task for a personal proxy. You can sniff traffic on the proxy and apply rules to modify requests/content