The body can be experienced as being light or heavy. What makes it so is down to a combination of factors - some related to mechanical use, and others related to focus of attention.
Mechanically, things changed for the worse when we started wearing shoes and adopted a heel-strike way OF walking and running. Our musculoskeletal system evolved for barefoot movement, in which the ball of the foot takes the initial load. Embodiment eventually comes back to our relationship with the Earth - and one aspect of this is how we use our feet.
Lightness is also something of a state of mind. Children do not experience themselves as being heavy, and appear to fly when they run. The apparent weight is very strongly affected by where attention is placed. If attention goes to heaviness, then the feeling is one of heaviness. If attention goes to lightness, then that is the experience. The focus of attention is always a choice - it's just learning now to shift that focus in a way that is "ecological" to the needs of the whole body.