Weight of a body is always because of its  gravitational attraction with earth.As law of gravitational attraction is universal so it applies to any two bodies (earth and sun as well).So we can define the weight of earth w.r.t a body of mass comparable or heavier than earth because of its gravitational attraction between earth and that body.But practically no body on earth has mass comparable to earth so weight of earth will be a meaningless concept w.r.t earth frame.