All of the sites I looked at said "heavy" or "a lot" or "42.3 pounds." Mjolnir was forged from a collapsed star (a white dwarf or a neutron star). This means it is insanely dense.
Worthiness aside, given its size (as seen in the movie) how much should it weigh?
Perhaps I should clarify. Given the average density of a collapsed star, if you took enough material to construct the hammer, how much would that item weigh on Earth?
Answer
There are two problems answering this question. One - what is the volume? Two - what form of collapsed matter are we talking about? The difference between the density of a white dwarf and neutronium is 7 orders of magnitude (factor of 10,000,000).
So let's assume, for the sake of making it possible to compute a number that the weight of 42.3 pounds was computed for some volume of mostly iron. 42.3lb would be 19.187kg which, would be 2.437l of iron (density is listed as 7.874 g/ml).
2.437l of white dwarf material (approximate density 1,000,000 g/ml) would be 2,437,000kg or about 2,686 US tons.
The Wikipedia article on white dwarfs lists a range of densities for neutronium. We'll use the low end (8.4 e13 g/ml) and this would give 225.6 billion US tons.
Obviously, as was pointed out, the hammer is routinely placed on top of ordinary objects that are not immediately crushed, if the hammer weighed that much. So either:
The hammer was forged of ordinary material and it's weight and/or mass are adjusted in real time by some magic to produce the desired effects.
The hammer really does have a massive weight but it's effective weight and/or mass are adjusted in real time by some magic to produce the desired effects.
The effect is the same, so it really doesn't matter, though one could suppose that the magic to reduce the weight of an object might be simpler than the magic to magnify it (or vice versa). If something like that were true, then my best guess is that Uru is something formed in the heart of a white dwarf and the actual weight is in the neighborhood of 2,000 tons.
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