Overall - great work thus far. Particle is really the gold standard in how the progression is and I like to use it as a baseline.
General feedback - Tachyon weaponry - Power efficiency is big thing for them - ok great, but there are some discrepancies. However, do not scale the AP anymore above 10. It is not needed and that is equivalent to 3D of damage but of less use vs lower armour targets. So it's an excellent mechanic, but scaling AP AND damage is over the top.
Smallbays - near flawless. Fusion and Tachyon need a gentle beating though - scaling way too fast. If we look at barbette vs smallbays:
Particle +2D +100% power
Fusion +5D, +150% power
Tachyon +3D and +5AP!! +0% power
Tachyon Power is a no brainer (maybe +50%), but the damage and AP is a huge gain for a weapon with excellent range. Smallbay Tachyon should go +2D, but no AP. Therefore being 3D, 10AP.
Fusion needs to scale a little less quick to avoid massive amounts of later, so perhaps +3D, resulting in an 8D small bay (and flowing nicely into a 1DD medium bay)
Medium bays - some items here that are apparent from number crunching (I can share the excel sheet)
Fusion bay - 2DD is monstrous (and awesome). Even then, going from barbette to smallbay (+5D), damage doubled, at the cost 150% power. However, going from 1DD to 2DD... is only a 50% increase? This is very much off.
Recommend that Fusion smallbay is 8D, and medium bay is 1DD - with the current costs thats a bit more understandable.
Tachyon Bay - +2D from smallbay, and same AP. This would mean medium tachyon bay is 5D 10AP. The current version has it as a monstrous 11D - and TL16 molecularly bonded armour won't exist in most universes.
Large bays
This category is becoming a little of a pet peeve (sorry Matt) - but I honestly dont mind trying to make it work. The danger with us constantly increasing damage-per-hit, is completely undermining ship protection value (such as armour, screens and so on).
Regardless, lets take a look:
a) We definitely dont need these babies to fire twice, for the love of God!
In addition to having to worry about these weapons blowing past screens and armour, you will have to worry about using more thrust to try to avoid the blast! So this is not needed - they're powerful enough on their own.
b) Fusion, if we look at slower scaling for small/medium can be a nice, huge 2DD here - not the 4DD (wowzers) that it is now. Honestly, at 4DD its close to par with spinal weaponry that are TEN times heavier.. so I'd definitely look at having a threshold for Heavy bays at 2DD tops. This threshold would belong solely to the Fusion Bay.
c) Tachyon Bay, due to the large size increase, I can see this remaining at 8D. however, as mentioned before, you definitely dont need more than AP10. If you want slightly more effective, you can consider 7D AP15 - but even then - thats ignoring all OTU armour and doing 7D.
Aaaannnd thats it!
I think it's key to realise that even if we decide to stay with Heavy Bays (grrr but I'm open minded
) - their MASSIVE value is inherent in their ability to do ridiculous damage in a single hit. They SHOULD be inefficient as that value is not easily countered.
I haven't looked at inefficiencies in power in detail but once we have some the damage-sanity changes in place, we can look at the finer details of how much power should this shot be drawing...
General feedback - Tachyon weaponry - Power efficiency is big thing for them - ok great, but there are some discrepancies. However, do not scale the AP anymore above 10. It is not needed and that is equivalent to 3D of damage but of less use vs lower armour targets. So it's an excellent mechanic, but scaling AP AND damage is over the top.
Smallbays - near flawless. Fusion and Tachyon need a gentle beating though - scaling way too fast. If we look at barbette vs smallbays:
Particle +2D +100% power
Fusion +5D, +150% power
Tachyon +3D and +5AP!! +0% power
Tachyon Power is a no brainer (maybe +50%), but the damage and AP is a huge gain for a weapon with excellent range. Smallbay Tachyon should go +2D, but no AP. Therefore being 3D, 10AP.
Fusion needs to scale a little less quick to avoid massive amounts of later, so perhaps +3D, resulting in an 8D small bay (and flowing nicely into a 1DD medium bay)
Medium bays - some items here that are apparent from number crunching (I can share the excel sheet)
Fusion bay - 2DD is monstrous (and awesome). Even then, going from barbette to smallbay (+5D), damage doubled, at the cost 150% power. However, going from 1DD to 2DD... is only a 50% increase? This is very much off.
Recommend that Fusion smallbay is 8D, and medium bay is 1DD - with the current costs thats a bit more understandable.
Tachyon Bay - +2D from smallbay, and same AP. This would mean medium tachyon bay is 5D 10AP. The current version has it as a monstrous 11D - and TL16 molecularly bonded armour won't exist in most universes.
Large bays
This category is becoming a little of a pet peeve (sorry Matt) - but I honestly dont mind trying to make it work. The danger with us constantly increasing damage-per-hit, is completely undermining ship protection value (such as armour, screens and so on).
Regardless, lets take a look:
a) We definitely dont need these babies to fire twice, for the love of God!

b) Fusion, if we look at slower scaling for small/medium can be a nice, huge 2DD here - not the 4DD (wowzers) that it is now. Honestly, at 4DD its close to par with spinal weaponry that are TEN times heavier.. so I'd definitely look at having a threshold for Heavy bays at 2DD tops. This threshold would belong solely to the Fusion Bay.
c) Tachyon Bay, due to the large size increase, I can see this remaining at 8D. however, as mentioned before, you definitely dont need more than AP10. If you want slightly more effective, you can consider 7D AP15 - but even then - thats ignoring all OTU armour and doing 7D.
Aaaannnd thats it!
I think it's key to realise that even if we decide to stay with Heavy Bays (grrr but I'm open minded

I haven't looked at inefficiencies in power in detail but once we have some the damage-sanity changes in place, we can look at the finer details of how much power should this shot be drawing...