This is a revised tier list based on further testing with every weapon type. A lot of things are going to shift around, but the core of the upper tiers is going to remain largely the same.
Biting Edge: The only reason I'm not rating this at S++ or SS now is because that'd skew the curve. But couple the BE with Deep Breath (BRT 13mm BCU) and, at burst 3 and 150 ST, you can get ~18 seconds of Halo Assault spam with only 1.5 seconds of recovery time. If you're a MADMAN, you can run minimum ST for less attack time but even less recovery time. Deep Breath makes this weapon aggressive to the point of an angry ex-girlfriend. BRT is mandatory, obviously—AIR might seem tempting, but Petal Frenzy actually lifts you up, meaning you can't lengthen your combo with an air jump as easily as you can with a Lunar Orbit combo with HM.
Heavy Moon: It's the meta weapon for a good reason. It's safer than Biting Edge with no need to worry about ST management, but the damage output isn't nearly as high. The HM's greatest strength comes from its ease in Downing aragami with Lunar Orbit and following up with Apocalypse Axe, which can hit for 10-13k damage on a broken part w/ OO element on an aragami weak to that element, making you capable of such shenanigans as timing a Down to completely bypass Dyaus Pita's transformation. AIR and BRT are ideal BCUs, or MPW if you're confident in your ability to not get hit (this applies to every weapon, though, so I won't include it from here on out).
Boost Hammer: A surprising addition to the meta. Specializing exclusively in burst damage (i.e. powerful single hits) with proper use, the BH's high Crush stat lets you break parts and Down easily with proper positioning, letting you unload with BAs like Grand Finale and Lost Memory for massive damage. Lost Memory is going to be your primary damage dealer—just spam air triangle attacks. BRT is most ideal for utility due to the combined stamina loss of jumping (for air triangle attacks) and Boost Driving for Boost Impact spam with Grand Finale—letting you be more aggressive with less recharge time—you can also go with AIR, but the recharge speed of BRT gives you functionally more damage per stamina unit per time, if that makes sense.
Buster Blade: Only if you're good at Parrying Upper. Anathema is a very high-damage BA, but only being able to use it when you're being attacked reduces its utility and overall damage potential.
Long Blade: While my previous remarks still stand, Void Cutter is more a novelty than anything. It's still superb at targeting weak spots, but the damage isn't high enough to warrant using it over any of the higher-tiered weapons. AIR is necessary here, and Apsara Wings into Void Cutter should be your bread and butter—unless you want to use Swift Slash for higher burst damage. The lack of an increased damage option vs. downed foes hurts this.
Charge Spear: High burst damage and utility with Charge Glide BAs make this a safe weapon to use in dangerous solo missions (like Elite 19/29), but the necessity to charge up and then recover from the CG animation, coupled with aerial CG being tricky to aim in many situations, chop a few points off of this weapon's overall usefulness. No BCUs really stand out here, so CST is a safe option.
Buster Blade: Without Parrying Upper. BB has high crush damage and ability to break parts, so most of your damage will come from using Overkill on a downed foe. Outside of that, Deadly Glide-air devour combos are your bread and butter. AIR is necessary here.
Short Blade: Nothing has really changed here from my last tier list. Optimum play is Licht Kreuz - air devour - air step combos to maintain air superiority (and remember to make use of your infinite air steps), but even still, your damage output won't be as high as with other weapons. Rampaging Comet is another option, but unlike Astral Dive, the angle is much flatter (less vertical/steep), so it's harder to aim. AIR is the obvious BCU.
F Is For Fuck Tier
Variant Scythe: Update 1.2 relaxed the timing for Hell or Heaven, but that's still not quite enough to allow the scythe's damage output to match up to other weapons. If you insist on using this, VSS BCU is mandatory.