you know, I was thinking of what those weights can be made out of, depleted Uranium is the heaviest natural element, but it's still a little radioactive and rather soft to make weights out of. Lead is the heaviest element that's not radioactive, but it is still very soft, not to mention BOTH of these things are heavy metal toxins so the weights would simply be dangerous to touch or even be around. But if they were made out of lead and then coated in plastic or something that would prevent it from coming into direct contact with people then it might be safer, assuming they didn't rip themselves off the bar because of their weight...(again falling back on the whole too soft thing.) OH OH OH! How about Tungsten? It's a little lighter than lead but still really heavy and much harder. It might be a little brittle so if she dropped it they might shatter, but I think you can make a plate out of that stuff
Lead is perfectly safe to handle for brief periods of time. You wouldn't want to make jewelry out of it, but handing lead weights is no problem. Given that it's also about 700lbs per cubic foot, it looks like a good contender for the weights on Anvil's bar. The REAL question is what the BAR is made of, since ten weights on either side means a total of 8 tons(!) total. The bar is very well reinforced, but even a steel I-beam that width would probably be pushed to its limits to hold that much weight.
So people with natural superpowers look like parodies of the human ideal, but Sydney gets her powers from her orbs, I'm guessing a magical artifact of some kind, which is why she's normal...is that going to be a thing in the comic? Are we going to see more normal people getting their hands on some maguffin that gives them abilities?
I love how Grrl Power is more realistic than most superhero comics I've read; I don't think I've ever seen She-Hulk use a reinforced bar to prevent bending. I'll bet Archon also reinforced the floors to withstand the pressure of 16,000 pounds of force concentrated over the area of her feet.
I remember a comic where the She-Hulk had been hypnotized by Ringmaster from the Circus of Crime. Before that, she was weightlifting a pair of elephants on platforms. In the comic, she said that she had to concentrate more on keeping the bar from bending out of shape than the actual lifting. So, while not quite as realistic, they do keep that kind of thing in mind.
Depleted Uranium is slightly less dense than Tungsten (19.1g/cm3 vs 19.25g/cm3) but for the US government, probably less expensive. The downside is that DU is Pyrophoric and as such if someone's power goes wild you could end up poisoning/incinerating all the non-invulnerable people in the room.
I don't know about the other ones, but platinum in general (at least as it's used for jewelry purposes) may very heavy (and freaking expensive!), but it's also soft. You can poke a pin into a platinum band and leave an indentation. O_o Weights made of platinum probably wouldn't be round after the first time they're dropped to the gym floor.
We don't forget about them, we just remember that they're really expensive. Iridium is one of the rarest elements and as such manufacturing a set of weights from them just so that they can be a little smaller than ones made from cheaper Tungsten would probably be viewed as a waste... Even by the US military.