I think you've done an awesome job of animating him so far, while the movement is very over the top i think it has a certain character to it. I like that you have animated his whole body moving when he runs, maybe just lighten up the arm at the back? Looks like someone else's arm.
You've also formed his body well but the bulkiness in his idle doesn't seem to match the bulkiness in his running. I went ahead and did a quick edit of the first frame of his idle:
I changed his skin color palette to define his muscles a little more and used the shape of a later frame for his shoulder and arm positions as he looks bulkier that way. I think that if you used that as his base frame instead and then animated from there he will look more buff and less stretched upwards. I also moved his pecs up as his pecs probably shouldn't be hanging so low and also added a little edging around where his abs would be. Also smoothed out his shoulders a bit and added a couple pixels on his left arm (on the right).
The most important thing I changed though was his hands. They kinda looked like a confused mess of pixels and I gave them some shape. When ever I do hands, especially when it's a fist, I focus on the direction the fingers flow a use the lightest color to create that direction and the darker colors to define the "holes" or concave parts of the hand.
For some example on hands, while they might not be very good, below are some animations I did a while ago (the last one is supposed to be him treading water). I think the hands are best defined in the jumping and the swimming where you can see closed fist from different angles and open hand from different angles.
I hope some of this helps!
