Who invented the Beam Balance?

Answer 1

I think it was invented by Mr Beam.

The question is whether you are you refereeing to methodology of determining mass or gymnastics.
If this is the first case then I think beam balances were invented long before the wheel.
It suffices to say that it was long before recorded history. In the western world the theoretical aspects probably would belong to Archimedes but I suspect the balances existed long before him.

If the second case then see ref below