Remember, the key is to identify drivers, estimate the value, and use good judgement throughout.
Here's what I would do:
Assume the majority of the weight will be the metal structure, not the stairs or the screws or the concrete base. So we should focus on the weight on the metal.
Weight = density x volume for each "bar". Density we would look up in real life, but for now we have to make some assumption. So now we have to estimate the volume of each bar and the number of each bar.
Volume is the interesting part. Volume is area x height. For Area, let's assume that all "bars" are 1 square foot, although for sure some are more and some are less.
So we still have to estimate the height of the bars. How tall is the Eiffel tower? Maybe 300 metres? Maybe 1000 ft? So we can calculate the volume of each bar.
Finally, the number of bars. If I'm picturing it correctly in my head, we can say that the tower has 4 legs is made up of 4 vertical bars. So total of 16 verticle bars, each 1000 cubic meters of volume.
There's probably also diagonal bars. Maybe assume that for each vertical section of 4 bars there are 8 diagonal bars (making an 'X' shape up each side of each leg. Assume they are like the hypotenuse of a right triangle so are approximately 1.4x as long as the height. So it would be the equivalent of 8 x1.4 ~11 for every 4 bars. So for the 16 vertical bars there will be 4 x 11 = 44 diagonal bars. Therefore 16 + 44 = 60 bars of 1000 cubic feet. There's probably also some horizontal bars, but let's assume these are thinner and negligable.
Now, I just multiplly it through: 60 x 1000 x Density. Assume density of 250 kg per cubic foot. Why 250? I'm trying to picture a solid cubic foot of steel and how many people it would take to lift it. If each person can lift 50kg, it would take 5 very strong people to lift, yeah that makes sense.
Okay, so 60 x 1000 cubic feet x 250 kg per cubic foot. So, multiply the last two terms first because it gives you a nice round number: 60 x 250,000 kg. We know that 6 x 25 =150. So 60 x 250,000 kg = 15,000,000 kg.
I'm trying to sanity check that, doesn't seem unreasonable.
Voila. That was fun. I have no idea if I'm right (or even in the ball park) but if I'm not, you can probably tell me which assumption(s) I made was incorrect, and fix it, which is exactly what is the point of a market sizing question.
Happy to help more, just message me!