So, new deep metals?
The current one will just not cut it (pun intended) for hammers and maces.
A light hammer would be a little counter-productive.
First thing that occured to me is that real life warhammers tended to have pretty narrow, reinforced striking points. We could then say that the stronger the material, the more narrow the striking point becomes, and therefore more force is applied.
Or, you could have blunt weapons respect the 'Hardness' of the material, and we could assume that the harder the material, the more it's able to dole out force.
On another tangent altogether, we could say that dwarves are so hardcore that they weight their hammers with big effing rocks, and the stronger the metal the bigger the rocks and the heavier the hammer can be. You'd get massive honking adamantine hammers that only superdwarvenly strong individuals could wield.
The better the metal the bigger the weapon isn't a completely outlandish concept, actually. It was the limiting factor restricting the length of swords for much of human history. Copper, bronze swords tended to be rather short, and then the stronger the metal the longer they could make the swords. Any swung weapon will have more effective velocity at the tip the longer it gets, and therefore it becomes more damaging.
So we would see warhammers with short hafts and less heavy heads with copper and bronze, and the stronger the metal the more you can increase its size, or add heavier rock or lead in order to increase its effective weight, with the overall structure able to handle the strain due to the superior materials like steel and adamantine.