Once you have a block of it its not difficult to grind it using the correct wheel, that's how the sharpen tungsten cutting tools
Sure, and you can drill it using ultrasonic techniques. But these are expensive ways to fabricate a shape; I guess the question is if the saving in effective mass is worth the extra expense.
Here is a simple argument:
We start off with a symmetrical arm, with a 9" (or 12") counterweight stub, and a mass equal to cartridge and headshell at the end of it. This equals the effective mass contribution of the front side of the arm, and doubles the total. Now we halve the stub length, and double the mass at the end - this still balances. But because the effective mass goes like the square of the distance from the pivot, the doubling of counterweight contribution is more than overcome by halving the distance, so the back end is now only contributing half as much as the front. If we make the stub length (to the middle of the counterweight), a tenth of the arm length, then the backside contribution is only a tenth of the front, and we are into the law of diminishing returns. The counterweight needs to weigh about 10 times cartridge and headshell (plus a bit for the arm tube); this might be 100g or more centred at about 2 and a bit cm from the pivot. Using something like lead (or brass or steel), this is maybe 10cc of stuff (maybe 12cc for brass or steel), This could be a cylinder an inch in diameter and an inch long (roughly). This example could be pushed, with a bigger weight closer to the pivot; this make take you from a 10% effective mass contribution to 5%, leaving a bit more mass budget to use on rigidity in say the head shell area.
These numbers are just hand waving for examples; you need to do the calculations properly using integrals as the object sizes are comparable to the distance from the pivot.
Using a higher density material allows a bigger weight to be placed closer to the pivot but you can see it only makes a small difference to effective mass; you need to work the numbers properly for a detailed design.
I guess the other issue to bear in mind is that very heavy weights load the bearing hard; at some point this loading will cause trouble.