You can consider notifying about your site updates on social media (Twitter, Facebook etc.) as soon as you post. The timestamp recorded there can be a fair indicator that you wrote first.
Assuming, popular search engines already index your web-pages regularly (use the site operator, site:example.com
, to find out) the date in the cached copy can be used as a rough indicator of when the content was published.
Update: Through Google Webmaster Tools, you can enforce a setting to have Googlebot crawl your site too often or manually ask Google to crawl a specific page or site.
As this article suggests, you can write a polite email to your competitors to desist from copying & then if that doesn’t help, send a formal DMCA letter to his web hosting company and also possibly to his advertising partner(s).