To get started, install the extension and pin it to your toolbar. 

Now, start browsing your Roam database using Chrome to build up an index of backlinks. Once you've visited some Roam pages, try opening one of the external links (not a [[Roam Page]]) in a new tab in Chrome and you should see a small box with the number 1 appear on the extension Roam Backlinks icon. This means that there is 1 backlink for the current page. 

Clicking on the Roam Backlinks icon in the toolbar will bring up a popup window which shows you the backlinks and allows you to click on them. 

If Roam is still open in another tab, clicking the backlinks will automatically open them in that tab. This is especially useful if you have a computer screen that is large enough to fit two browser windows side-by-side.  If you want to force a backlink to open in a new tab you can use the middle button of your mouse to click it.

Thanks to some ingenious code by @ViktorTabori, you can also shift+click to open pages in the Roam sidebar if Roam is already open in a tab.

PRIVACY INFO: This extension indexes your Roam database one page at a time as you visit each page and stores all the data locally so that none of your Roam database ever leaves your computer. If you uninstall the extension, the index will be completely deleted. The extension uses Google Analytics to collect anonymous aggregate statistics about how many people are using the extension. No private data ever leaves your computer.