Hi Dan
You need to calculate the volume of the dagger, and then multiply by the density of the material.
Break up the shape of the dagger into solid forms which are easy to calculate the volume of. The hilt-side half of the blade (the strong) is roughly a diamond-shaped prism (formula V=l*t*w/2), from half-way to the tip is roughly a flattened pyramid (V=l*t*w/6 I think). The grip, pommel and even the guard could be roughly approximated as equivalent rectangular boxes (V=l*w*t).
Calculate each one (where l is the length of that part, w the width and t the thickness) then add all together.
If you multiply the volume of each bit by distance from the back of the pommel to its center, then add them and divide by the total volume, you'll get a
rough idea of the distance from back of the pommel to the
center of gravity.
As an aside, surely a steel blade is cheaper than a larger bronze casting? I was under the impression that bronze-casting was very expensive, and the more so the bigger (and more complex) the piece. By mass, bronze is certainly more expensive. A steel blade could be fabricated entirely by
stock removal using hand tools, I'd have thought? I am an amateur, of course, so I'm not familiar with the economics of professional knife-making.
I hope the formulas help
Regards
Andrew