[Fyron]

damage / size / rate

is the main formula for comparisons. You can't really factor range into it mathematically, because the effects of different ranges are very complex. They vary based on ship speeds, your to hit bonuses, the enemy's defense bonuses, etc. The same applies to factors like raw to hit bonus of the weapon. A weapon with a 10% bonus to hit isn't really 10% more powerful; in cases where you have higher hit rates, 10% bonus is very small. In cases where you have low hit rates, 10% can make a difference. Supply usage is a nice balancing factor (have heavy supply usage, strong weapons for system defense, and lighter weapons for long range tactics), but it doesn't factor into damage ratios mathematically. Same with cost; its a factor in economics, certainly, but weapons usually aren't the vast majority of the cost of ships. You can't really factor such things into one single formula.

This is why SJ's weapon stats program uses a bunch of different formulas to generate a wide array of stats; different formulas are useful for comparing relative strengths different situations. There is no single formula to rule them all. Balancing weapons is a complex affair that requires much play testing. Math can get you a good baseline, but it won't do everything for you.