Wrongest's idea about 'squishiness' is right-on. Also, you could try having the whole upper body slide down the hip joint a little on the downstep, like gravity was yanking his girth down further while the leg is stopped by the ground.
What I think might work with the guy's physique, is if he kinda squished every step. But that's a pretty cartoony effect. Depends on what you're aiming for.