Is there a way for a user of a site (no database) to add their own notes to a webpage, so when they return (regardless of the device), their notes are shown?
There have been plenty of attempts at building web annotation systems like this in the past—I actually built one for my final year university project a decade ago—but they all suffer from the same problem: web pages change, and once they have changed the annotations may no longer be attached to the right place in the document.
They also tend not to cope well with modern single-page web applications, where a single URL can correspond to lots of different “pages” within a site.
I would suggest using a bookmarking service like http://pinboard.in/ instead, which lets you save links (publicly or privately), add a note to them and optionally add tags as well to organise them.
If you’re determined to do in-page annotation, here’s a list of tools I just found: Top Web Annotation and Markup Tools