The question of one eye being weaker than another is something I've had to grapple with myself.
When I had my initial vision drop, my weaker eye dropped more than my stronger eye to where they both became the same. I did lots of looking down at the ground then looking into the distance alternating glancing outside, moving my head up and down slightly instead of my eyes. Down-straightahead-down-straightahead-down, etc. At most a second for each one.
My belief is that the long swings side to side are better when the eyes are equal, or at least under half a diopter difference between them. When the differences between the eyes are more than that, I prefer the alternating glancing I described, which forces your eyes to work together more by virtue of the "swing" being vertical(up and down) in the center of your field of vision.
I don't like covering an eye with your hand when reading the snellen or anything else for that matter. After being balanced for a little while, one of my eyes is now .25 weatker and every time I cover my stronger eye with my hand, it always seems to weaken the vision in my stronger eye just a tad. So I either close my strong eye or iif U use my hand, I cover it for only a second at a time.