The magic of the hammer makes its weight arbitrary. Consider that weight is the force on an object due to gravity, that means that we have to take into account the mass of the hammer and gravity(a constant). However, the hammer doesn't adhere to physics as we know it.

At one moment it can be wielded by Thor, set on a table without breaking the structure, and fly through the air. At the next moment the Hulk himself, who we know to be exceedingly strong can't lift it up. If we attribute these instances to its weight changing, then it can obviously be any arbitrary weight necessary. (Technically we don't know if there is an upper bound but as it's magic it is safe to say there is, in so far as it is convenient to the plot). If we attribute them to some force other than a change in weight, the weight still becomes inconsequential, as it still performs the same way as if it did not have weight.

To reflect on your edit:

From the transcript

Forged in the heart of a dying star, from the sacred metal of Uru...

I think this is saying that the location of where the hammer was forged is in the "heart of a dying star", not that it was forged from the dying star. It is a common idea in a lot of literature to say that an object (sword, spear, shield, hammer) is stronger when forged in a hotter furnace(not being a blacksmith I can't attest to this but it makes sense), I imagine that this is just a matter of Odin indicating that the heat required to forge it came from a dying star.