The Eiffel Tower isn't very heavy

The lattice structure of the tower generates strength out of proportion to weight:

...The most startling piece of trivia that I’ve heard about the tower is that it weighs less than the cylindrical column of air that it sits in! That’s right, if cylindrical tube were placed over the tower, the weight of the volume if air inside the tube would exceed that of the metal in the tower...

The density of wrought iron is approximately: 7.70 g/cm³

At a weight of 7,300 tonnes, this amount of iron has a volume of approximately: 948 m³

• If melted down into a sphere of iron, this ball would have a radius of just 6.1 m
• If flattened into a coin with a diameter the circumscribes the base of the tower, it will be just 4 cm thick!

...Using the dimensions of the foot of the tower, the diameter of the cylinder can be calculated...

Knowing the height of the tower, combined with the disc diameter we determined above allows us to calculate the volume of the cylinder. There is approximately 7.96 million m³ of air in this tube. [adjusting here for the varying density of air at different altitudes] ...we can take a simple average for the density of the air to give a value of 1.19 kg/m³.

Multiplying by the volume we get a value of approx 9,400 for the mass of the air. Even with our approximations, this is certainly greater than the quoted 7,300 tonnes for the mass of the iron.

It's true - the mass of the air in the cylinder surrounding the Eiffel Tower, is heavier than the tower itself!