Zotero has been mentioned in this thread a few times, and it has this feature. The browser extension has both "with a snapshot" and "without" options (the snapshot being your local copy), and you can choose the default and also choose for each page if you want to.

(It does have some idiosyncrasies since it's supposed to be a citation manager originally, but once you get used to the workflow it gets out of the way and works really well.)