As demonstration of the economy of design, if the 7300 tonnes of the metal structure were melted down it would fill the 125 meter square base to a depth of only 6 cm (2.36 in), assuming a density of the metal to be 7.8 tonnes per cubic meter. The tower has a mass less than the mass of the air contained in a cylinder of the same dimensions, that is 324 meters high and 88.3 meters in radius. The weight of the tower is 10,100 tonnes compared to 10,265 tonnes of air.
Stole this from the Eiffel Tower wiki. Read it, its cool.
PS. I forgot to add that we took the stairs down from the second level, legs felt wobbly.