Syndicating your content to other sites and blogs in your industry can be a good way to build up traffic to your site, and pick up some backlinks.
I would recommend being selective with this though, as although Google will normally recognise your site as the original source, there may be times when due to the authority of the site hosting your content they may actually outrank you.
Aside from seeking other sites to repost your content (either manually, or through an RSS feed), you might want to think about actively encouraging visitors to republish your posts (with attribution, i.e. a link). If you go down this route, you can throw up a creative commons license for your content, instructing those who wish to republish exactly how you wish to be credited.
The viral sites do this all the time
IFLscience (I'm sure you know what the IFL stands for!) is a high traffic site that often republishes articles from elsewhere on the web.
In fact, the viral sites (buzzfeed, distractify etc) are full of content that is just repurposed from elsewhere with a ' via' of ' h/t' (hat tip) link at the bottom.
If buzzfeed take one of your articles and republish it, then believe me the traffic you get will more than make up for the plagiarism!
Of course, if you find someone using your content without attribution, then reach out and ask for a link. If they don't acquiesce to your request, then you'll probably want to consider filing a DMCA takedown.
Automatically add a link to copied text
If you are using wordpress, there are a number of plugins available (such as this one https://wordpress.org/plugins/add-link-to-copied-text/) that will automatically add an attribution link to copied text.
This can be an easy way to pick up some extra links, with no additional overhead required on your part (other than 2 minutes to install the plugin).
Further Reading
Recommended Tools