there's no forward momentum in the body (hips and shoulder movement) also when we walk, it's a process of initiating a controlled fall that we catch with our moving legs.
When we walk, our heads will dip forward just a tiny bit on the impact of the leading foot, there is not just up and down motion, but slight forward falling and straightening as we catch ourselves, in most simple sprite animation, a lot of this is not captured because of insufficient pixels or strange use of style/proportions. Because you are drawing something more realistic, you need to emulate life more.
In addition to the forward falling of the head, the hips will also move forward just a bit to catch the fall, what you've got in your animation is a straight up and down motion, and I can see the legs in the figure growing longer to impact, it's giving it sort of a piston effect. Rotation of the hips will compensate a little but movement of the upper body in reaction to the change in balance is what will eliminate the weird look.