PointStaggerDelay
This is the delay between the emitters on the ship firing. For example the Kol's beams. It's one weapon that has 4 firing points on the front of the ship. This variable controls the amount of time between each emitter firing. 0 should mean all 4 fire instantly, increasing the number staggers them a bit.
burstCount
How many "bursts" the weapon fires in a single shot. This depends on the weapon's particle effect. The Vasari LRM frigate's burst is 1 missile. If you set the burst count to 2, it will fire 2 missiles. This is independent of the damage dealt, it's purely a visual effect. It controls how many particles the weapon fires. You can use this in combination with burstDelay to create constant autocannon fire, for example, without changing the damage output.
burstDelay
The time delay between the bursts firing. In the example above, if you set the Assailant's burstCount to 2 but burstDelay 0, the 2 missiles will fire at the exact same time. Increasing the burstDelay will delay the second missile firing so it will look appropriate.
WeaponType
These are the weapon names as you see on the info cards. Autocannon, Projectile, Missile, Beam, Wave, etc. Those are the only ones you can use.
AttackType
This is the type of attack it deals for purposes of damage percentages. It applies to the DamageData chart in the gameplay.constants file. So "ANTIHEAVY" attack type will do 150% damage to heavy armor targets, 50% to very heavy armor, etc as defined by the table.
DamageAffectType
This allows you to control what the weapon can damage. The default for all is shields and hull, but you can do affects only shields and only hull. I know you can do hull only for a fact, pretty sure you can do shields only.
DamageApplyType
This is how the weapon applies its damage. Instant, over-time, etc. The Kol's beams are over-time, they keep damaging the target at intervals while firing. Missiles do one time damage, on the other hand.
DamageType
One of the less relevant settings, it's either physical or energy, I don't think there are any other settings. You won't get much use out of it, other than there's an ability trigger to make ENERGY weapons fire faster. The same does not exist for PHYSICAL.
WeaponClassType
This is used internally and generally tied to research affecting the various weapon classes. For example, weapon class BEAM can be linked to beam-specific research:
researchModifier
modifierType "WeaponDamageAdjustment"
baseValue 0.000000
perLevelValue 0.050000
linkedWeaponClass "BEAM"