Of course!
If it's at all helpful to you, I, on sheer curiosity, did some basic number-crunching for the weapon damage output throughout the core roster. For all of the procedural uncertainty we encountered in the game, the biggest hazard to it and motivator for us to finish up was, ultimately, the sheer damage imbalance at play. (Plus, having these numbers available to present to the reader as average guidelines would help for the matter of eyeballing objective health totals, alongside the other advantages of it.) There are other parts of the game I could get into in more detail, if that would help, I especially imagine Classes and Armors have their own (more difficult to assess) imbalance points, but, this is what I prioritized:
Ten Thousand Year Reign Shattering Blade: 6-24 (15) to likely one target. The weapon action allows a multitarget attack, which can buy back the action cost of activating it, but it's inconsistent even with the Compel. The weapon action never proved useful in play for us. The free attack on killing an enemy also usually never triggered, it seems like it could work as a Swarm killer, but only before they actually go and swarm up, which they usually had ample time to (or even spawned pre-Swarmed-up, something the GM was unsure if it was kosher or not).
She Speaks The Language Of Kings: 5-23 (14) to 3 targets. The weapon action halves damage, but extends range by targeting through allies. Just for the spread damage, this is essentially triple the power of the Shattering Blade.
Sethian Externalized Annihilation Cannon: 8-33 (20.5) to likely one target. It was rare that enemies would be clumped up in a way for the pattern to mean much. It does significantly increased damage vs Swarms, usually benefitting from eschewing Breaker since 10 damage per broken Swarm segment is a fair bit less than the expected damage. This weapon seems to hit notably harder than most, and if it weren't for the extreme outliers of damage, I would pen it as presumably ahead of the curve. The weapon action seems minor, since Blazing is only 1 damage total - I could conceive of trying to use it efficiently to spread to adjacent targets, but instead I could just use the AoE to hit said adjacent targets for 20.5 damage, which is, again, ahead of the curve for most damage.
Regrettable Precaution: 6-21 (13.5) to likely one target. The weapon action can maybe extend to multiple targets, but even then I doubt more than 2. The primary value of this weapon is that it can be fired as an Aux Action, and the upgrade tree offers the ability to equip a second weapon, making it an obvious "sidearm" choice. As a direct upgrade to player power, this makes sense, except, 13.5 average damage hits roughly as hard as some of the main weapons, making it almost a doubling of the average damage output. Tripling, if Support Actions can be downgraded to Aux Actions - can they? It seemed like no on a reread, which is something we ran wrong, but we might well have missed something or had something omitted. For the purposes of this post, I will assume that isn't possible. In principle, however, this upgrade makes it the "obvious" choice to the point where I'm not sure if taking any other secondary weapon would be worthwhile once this upgrade was unlocked? I suppose the idea is to help the Hellpiercers' damage match the amount that the HALO units unlocked in the same upgrade can do, but it does seem to me like it removes one of the dimensions of buildcraft to offer such a powerful and eclipsing option. (Especially since most secondary weapons are already limited in impact just by virtue of the time taken to swap.)
Heaven Burning Sword: Assuming actions cannot be downgraded as above, 15 damage to likely 2 targets. If they can be, 25 damage to likely 3+ targets. "Saving up" and only firing every other round is fairly worthwhile in a context with several small enemies to blast with the large AoE of the big hit. However, in contexts without several small enemies that aren't Swarming, which, in our experience, was not actually that common, 15 damage to one or two targets at the cost of an Aux Action is effectively a minor action tax on top of what most weapons could already do. If the Aux Action charge is doable while holding a different weapon for your Main Action attack, charging up passively could be a more effective strategy - except swapping back and forth also consumes Aux Actions, so it would be a rotation of four rounds between each firing, which means it's likely only once per combat anyway.
Ambiguous Intentions: The math for this weapon is complicated, so I'll eschew it in full here. I can highlight that the minimum possible output, if it does not run out of targets, and rolls two 1s on 2d8 six times in a row, is 15, which is already quite respectable (in fact, it's the damage norm the weapons seem roughly written to match, for the most part). Anecdotally, in our table, when it got a big enemy to circle around and hit in full, it consistently dealt in the 50-90 range. A pillar of 400 HP to be taken out over the course of 6 rounds as an objective was, to it, a difficult but entirely surmountable obstacle. This trivially eclipses anything else on the entire list, and, in the specific instance of scattered size 1 enemies it is difficult to combo-attack, the minimum effect of the weapon is still 2d8+3 + 2d8+2 - two hits that sum to an average of 23 damage. This is quite plainly the best weapon in the game, even when compared to the HALO weapons.
Sabaoth-Class Obliteration Charges: This weapon is difficult to assess as a weapon, since its primary use case seems to be as the main support option on the list, giving healing to allies in need. (Only 2 or 4, which isn't majorly helpful, but it is nice to have.) Used as a weapon, the best it can get is 10 to likely one target, or, at the cost of a limited charge, 16 to 2-3 targets. When combod with the Haphaestus Class it comes with, it can spam the 16 value hit as needed, which is actually fairly high-value of the standard vein weapons - that puts it on par with She Speaks The Language Of Kings.
Love Without Consideration: 2 damage. If the Lingering works perfectly, 4 damage. 3 damage if it uses the weapon action instead, since Blazing only deals 1 damage. This weapon could hit the maximum possible number of targets (4 damage to two targets and then 2 damage to two targets) and it would only barely be matching the damage output of any other weapon rolling an average hit on a single target. To be honest, I have nothing I could say in this weapon's favor.
Paradigm-Shattering Cauldron: 5-15 (10) to likely one target. Breaker doesn't really help it when there are other, better weapons that can get the tag. The effect to create a Void after an attack might be helpful in a party with a large amount of forced movement, but we actually didn't find too many options that could do that consistently enough to make it worth having less damage output the rest of the time, and there are other better ways of deploying Voids anyway. I think this weapon is under the level it needs to be.
Heaven Or Hell: The math for this weapon is complicated, and, unlike Ambiguous Intentions, it did not see play at our table to discuss in detail. I think I would need to see it in action to give a proper report, but, at a glance, the following seems to be the most damage output you can get out of one hit and the free tag you get:
Hit (3, gain Juggle) - Juggle (1, gain Pressure) - Pressure (1, push them into a wall, gain Bounce) - Bounce (1 damage to the target and another, gain Knockdown) - Knockdown (flip a coin, either 5 or you take 2, gain Pressure) - repeat from Pressure.
The consistent sum total of this combo is 6 damage, plus every Knockdown coinflip giving 7 more and costing you 2 health eventually. It also requires a target nearby to both an obstacle and an enemy unit. Throw and Knockdown's inconsistent damage makes their links in the chain implausible, but without them, your damage surely can't measure up. Due to the inconsistency of this weapon, it would need to have very high spike damage on the turns it does pop off to make it worth it. As-is, I don't believe the numbers can support that happening.
Consecrated Behemoth Spines: 5-26 (15.5) to likely one target. You get a small rider in terms of 2 temporary HP, which isn't much especially with Provoke considered, but it's the standard damage plus a nice bennie. The weapon action doesn't seem terribly useful, unless it's near the end of the fight and HP indeed does not reset between fights, but as a principled sidegrade to the Ten Thousand Year Reign Shattering Blade, there isn't much to complain about.
Her Tears Formed Our World: This is another weapon it's a bit confusing to assess. If the GM plays things principled, moving characters next to you to deny your damage buildup, you deal 2d10, 2-20 (11) to one target and 1d10, 1-10 (5.5) to another. A total of 16.5 damage, distributed to the GM's call of targets, so likely really you only deal 2 damage total to eliminate two 1 HP enemies and you get some solid mobility out of the deal. Alternatively, if allowed to build up unabated, at 6d10 you can average 33 damage on likely one but maybe two targets, which isn't bad - until you remember that it took you three turns of not attacking to reach that point, so it's only three turns of attacking later (the end of round 6) that you break even, only round 7 where you're in the black in terms of damage payoff, and fights likely are already over by then. This weapon suffers from the principle that damage sooner is worth more than damage later. Like Heaven Or Hell, I would want to see it in action before writing it off entirely, but as a fiddly choice that I'm not sure even makes par, let alone rewarding its complexity, I'm not very enthused by it.
In overall assessment terms, it seems like 15 damage is the average expectation for the output of a Main Action from one PC. This, in simple terms, makes consistent AoEs like She Speaks The Language Of Kings a direct power buff - one attack on three targets, rather than one attack on just the one. In a tighter weapon economy, without Ambiguous Intentions as an apex predator, it would probably be eclipsing the others to a notable degree. Some AoEs make it easier or harder to get multihits, so that distinguishes things for them, and weapons that can't hit for 15 seem to not have much use. Regrettable Precaution becomes a near-doubling of damage output with this math, which seems to me to be a rather large spike. The Annihilation Cannon is on the high end for reasons I can't quite figure out, it seems to me to just be numerically better. None of the weapons have riders that eclipse the value of their damage output itself, except for multiattacks and Ambiguous Intentions, to my initial assessment. Which also admittedly leaves some of them feeling rather samey, as slight variations of 15 damage with a rider effect that doesn't mean too much. I get the impression that 2 healing is expected to be substantial to some degree, but, considering the damage input we received in play, it didn't prove that way, so those end up closer to ribbons. None of these weapons offer a particularly long-range choice, beyond, again, She Speaks The Language Of Kings, and even that needs an ally to get up close and personal with.
I hope this number-crunching is useful, if there's anything else that's of interest in terms of what proved imbalanced or uncertain, I'm happy to elaborate.