Official comment
Google doesn't divulge what criteria they use for this behavior, even to us. Usually, images in Gmail are shown by default, at least since sometime in 2014. But even with images shown by default Gmail will sometimes require the user to click the link to display images. What's irritating is that even if you click the link "Always show images from XXXX", Gmail may still require you to confirm that the images should be displayed later. Anyone who tells you they know the reason why are guessing. Google will refer you to this long, technical document: https://html.spec.whatwg.org/multipage/embedded-content.html#images
With that caveat, here are some guidelines that might help. You'll have to test with your content to find the right mixture of approaches.
1. Use smaller images. If your images are larger than 20kb you have an opportunity to resize them to reduce the size. If your editor uses pixels, size the width of the image no larger than 700 pixels wide, the maximum most services believe should be used. You can use the free getpaint.net editor if you don't have one already. Our reasoning here is that with the growth of mobile devices used to check email, Gmail may be looking at image size and trying to reduce the impact on data limits on those devices.
2. Make sure you have more text than images, at least 60% text to image. If you are sending email that relies on images to tell the story you may hit the spam filter. We can demonstrate this pretty easily. It may also help with the issue of Gmail refusing to display images in an otherwise valid email.
3. Check the spam score we provide, and lower it below 3 if you can. This may or may not help; in general, a lower spam score helps overall.
I asked our postmaster if going through the process of setting up DKIM and SPF records for your From email address, to remove the "via ontramail.com" notice in Gmail, might help. He doesn't think so, but it is worth a try.