If object is too large or massive then only gravitational force is experienced but on the earth's surface large stone has not sufficient mass to pull the small one. The amount of force is too small or is negligible. Hence small piece of stone is not attracted towards the big piece of stone.

 Here the large stone is much smaller in comparison to the size of planets, smaller the object small will be the gravitational force produced by the object. The force of attraction between the large stone and small stone is so small that it is not possible to create motion in them. Hence, large stone does not attract small stone on earths surface.