In the framework of General Relativity, where the inertial frames are the ones in free fall, you can think that the Earth is accelerating upward, so it is not you who is pushing on Earth but it is Earth that is "running you over" because of its accelerated motion. Luckily enough, if we are standing on ground, we can avoid impulsive forces and our bodies are capable of sustaining a constant acceleration equal to $g$. The fact that we then cannot penetrate Earth as it accelerates upward is because the ground is pushing us up with a force equal to our bodies inertia.
So to make this a bit clearer, flies which are standing on the windscreen of an accelerating car will be squeezed against the windscreen like they have gained extra weight (the impulsive forces are those that would splatter any fly that wasn't already on the windscreen and that happens to smash against it because the car is moving towards them). Here we're focussing on the extra weight from acceleration alone, not on wind resistance.