Cool, I went ahead and made an edit as to how I would go about this and I did a few things:
1. The legs pick up less when walking, they don't go very high nor do they bend very much. I lessened that.
2. Similarly the arms just kind of sway. When a person runs they will manually move their arms, but walking just
naturally causes them to swing on their own. I straightened their arms more, though I did add a bit of an extra bend because this sprite is a little cartoony. Same with the legs, there is some exaggerated motion there.
3. I tried to keep the anatomy consistent. The knee needs to always be at the same place in each leg. The waist line should remain fixed (though the sprite bobs up an down, so the waistline should move along with it). Also I had to make sure not to deform the butt while changing the leg positions, ignoring the butt and treating it as if it were a leg can make it look floppy. Also make sure the limbs stay the same size as you move them
4. Lastly I made use of layers to make the animation symmetrical for each arm and leg. In the 8 frame cycle I literally copied each limb and pasted it in a new layer with an offset of 4 frames. I think it looks good and it makes life so much easier.

