When you share a post on Facebook, or when Jetpack Publicize publishes a post to your Facebook page, Facebook crawls the page and looks for Open Graph meta tags in the head to build a complete post preview (with an image, title, description, ...).
Jetpack automatically adds these meta tags to your site, unless you already use another plugin to handle Open Graph tags for you. Looking at your site, you seem to be using a plugin named "Open Graph Meta Tags for Facebook and LinkedIn Sharing". Jetpack consequently doesn't have any control over the images used by Facebook in its post previews.
As @plake777 mentioned, LinkedIn uses the same Open Graph tags to build its post previews, so the problem is likely to hit both platforms if your Open Graph tags are not correct.
To verify if the tags are properly set up, you can view the source code on your site, or use Facebook Debugger to see what Facebook sees:
It's worth noting that other site owners have also reported issues with Facebook in the past few weeks. Sometimes, even if the Open Graph meta tags are properly set up Facebook ignores them, or bugs with the image size as you've realized. Others have already warned Facebook about the issue here:
@plake777 You're also using a different plugin to manage Open Graph Meta tags. That image tag you mentioned is indeed the same on all your pages, but it is not added by Jetpack. I can't say for sure, but I think it is added by the All in One SEO plugin; I know AIOSEO was recently updated and added an Open Graph option, and you seem to be using the plugin on your site, so it could be it.