Let's state this for the record. I am not convinced that using the new image features on Twitter is the best way to go when it comes to marketing your business. It still smells too much like spam and if it's not handled properly it could do more harm than good.
With that said, there are definitely instances when it could do VERY well, particularly when it comes to gaining exposure and picking up more Twitter followers. The key is making sure you're keeping a 2:1 ratio aspect ration for your images.
They are displaying that way regardless of the size or shape of the image when seen in the screen. They can be enlarged, of course, but that's so old school. With the new Twitter feed displaying them inline without a click and the fact that they've added the engagement actions under each post across all of the platforms, it makes sense prevent people from having to click to see the whole picture.
Look at the example below, a tale of two Tweets. As you can see, the top image that I just posted fits perfectly into the frame that Twitter gives us. The one below it forces you to click through to see it. It doesn't matter how compelling the message is, only a handful of people will click to find out what the punchline was. They're much more likely to skip right past it, particularly if they're like the majority who check Twitter on mobile.
If your images are twice as wide as they are tall or close to that ratio, you'll be able to get the most impact out of your Twitter image marketing. Don't go out and make a bunch of ads at that ratio. Again, this can be abused and you'll turn more people off than ever before if you spam the system (and feeds). Keep it legit and everything will be just fine.