In the future it would be a good idea to state your references,

There is a reason this walkcycle works well enough while yours does not
JerkinessBecause of the small size, less frames are required to create non jerky movement. Try using 6 or 8.
Leg sizeEven at this small size, pixel has shortened the legs on the second jumping pose to keep with perspective
Arm consistencyOne of your arms has a hand that is 2x2 pixels big
For a character sprite this size, quote is probably not your best reference, using him will not nescisarily create a sprite reminiscent of cave story, as few players ever look into the frames of animation as i have such.
I suggest you decide wether you are aiming for a walk cycle or a run cycle
Choose good keyframes and tween frames
and ensure you have the movement required for a character this size
Here's a quick running reference i dug up
Runcycle, (nudity)There's a couple resources in the
Tools, Resources and Linkage thread for walk cycles