Chances are, from a purely SEO point of view, it would be more beneficial to have your site on mywidgets than on mywidget.
Whether or not its worth it financially will depend on how big a boost you get out of changing the url, and this will primarily depend on the competitiveness of the new keywords you are targeting.
If you do a quick google on "website widgets" or "free widgets", you'll see that the top few sites don't actually have 'widgets' in their domain name, it's 'widget'. This is probably because they're incredibly competitive search terms and those websites are simply far more authoritative than their 'widgets' competitors. The lack of an 's' in their names verges on insignificant in comparison to their massive backlink profiles which have been necessary to put them at the top of the SERP.
Including the 's' is likely to help, but don't count on it doing the job all on its own.
The worst thing that could happen is you go through all the trouble of moving and find that it hasn't made enough of a difference to justify the loss of traffic while moving. With this in mind, if I was in your shoes I would start by experimenting with Meta Titles and on-page copy on a few of my pages to see what difference that makes, before moving the entire domain - temporarily 301'ing mywidgets into mywidget.
One last thing to consider is that a 301 does not pass all the link juice from one domain to another. It's estimated that you tend to lose about 10% of the 'juice' in the redirect. Redirecting from mywidget to mywidgets will result in a more relevant, but less authoritative website.
Hope that helps
Devin