I notice that my site's ranking drops in Google if I leave it dormant for a week or two and jumps back up once I add new content. I was wondering if anyone had insights on if Google wants to see be a significant addition of new content or just any small addition to see that something has changed?
It's not exactly that your ranking is dropping. What of the huge number of signals used by Google in indexing and ranking sites and pages is the frequency of updates and how recently the site has been updated. Now not updating your site for a week or two isn't going to reduce your ranking, rather the other sites rankings are increasing as they may have new content.
As @Simon Hayter points out there is no hard and fast rule or magic number on how many articles per week or month should be added. It is actually to do with the number of interactions made with the site. A good balance that I have found is one new blog article a week or fortnight (the time doesn't seem to matter so much as long as it is reasonably regular) and as this attracts more readership to the site and in turn the potential for more linking and sharing this can help increase ranking as well.