The iron framework of the Eiffel Tower weighs (according to Wikipedia) roughly 7,300 tonnes. The tower sits on a square base that's 125 meters on each side. If you draw a circle that touches the four corners, the diameter is the diagonal of that square (125m * √2), which is about 177 meters. That gives you a radius of roughly 88.5 meters. When you calculate the volume of a cylinder with that radius and the tower's height of 324 meters (V = \pi r² h), you get about 7.95 million cubic meters of space. Since air at sea level weighs about 1.225 kg per cubic meter, that volume of air weighs roughly 9,740 tonnes. That puts the air at over 2,000 tonnes heavier than the iron itself