Double Vision (in my opinion) is (another) misnomer.
It gives the impression that you should see 2 objects instead of one.
In order for that to happen your gaze to one side should be fully paralyzed or there should be some serious problem in your visual cortex in the brain.
We normally see 2 non-identical pictures, because of the distance and alignment of our eyes. Our brain "knows" how to turn this into one 3-D picture. The muscles of our eyes allow us to move them in a way that the two pictures will continue to be aligned, even when we move our focus from the center to the side or up or down.
If we have weakness of one of the muscles that moves our eyes the alignment will not be as perfect. If this is constant, our brain can adjust to it, but if it is changing it can not. This will create "ghosting" and blurring of the picture. The smaller the picture is the more this will interfere with our ability to see it clearly. (that is why even increasing the size of the font or increasing the line distance can help).
Also, for some people there is also weakness of the muscles of accommodation. This kind of weakness normally happens with age (and can be easily corrected with eye-glasses), but when it is not constant it is hard to correct. That is why they will have "double vision" even if they patch one of their eyes.
I am having difficulty reading because it looks like the words are moving on the page and it is difficult to focus
This can happen because you are trying to compensate for the slight weakness of the eye muscles, by moving your eyes. (we normally move our eyes to get a better focus of what we are looking at). And this can make the weakness worse.
You can train yourself to move your eyes as little as possible, by concentrating on one word or number ( For me soduku was very helpful in doing that).
It took me time to find the optimal reading frame, in which the letters are big enough and yet I don't have to move my eyes too much.
It also took me time to find the optimal light that puts the least strain on my eye muscles.
I do most of my reading on my computer because I can easily adjust it to my changing needs. (as opposed to a printed paper).
And there are times in which I realize that what I should do is just close my eyes and let them rest.