i don't know if I'm saying this right, but on the first animation, it looks like the center of mass is changing rapidly when he hops up
don't worry about the character moving off the screen. if it happens, then you get to be lazy. i am 100% not saying that laziness is good. it's actually bad. if you want to keep him on the screen, shift EVERY frame. i recommend by 7 pixels. have fun!