Adding from my past posts.
http://m.neogaf.com/showpost.php?p=230472977
http://m.neogaf.com/showpost.php?p=230474743
I will summarise this here.
How much damage does a weapon deal?
(Atk*Multiplier) - Def = dmg
or
(Atk*Multiplier) - Res = dmg
So that is, your attack times the multiplier subtracted by the enemy defense or resistance which equals your damage. (Damage values are always rounded up when above .5)
Weapons triangle:
On the weapon triangle, red beats green, green beats blue, etc.
If you have a weapon advantage on the weapon triangle, it will increase your attack by approximately 18% or 1.18 for your multiplier when you want to calculate it using the formula above.
If you have a weapon disadvantage on the weapon triangle, it will decrease your attack by 18% or 0.82 when you want to calculate it.
Same weapon colours give a multiplier of 1 so it is neutral.
Effective weapons:
If you are using a weapon that will be effective against a unit type, it will increase your attack by approximately 48% or 1.48 when you want to calculate it.
This includes weapons such as bows, poison daggers, armourslayers, hammers and heavy lances.
When armourslayer which is red fights against a green armoured unit. The multiplier increases from 1.48 to 1.76 so you have a 76% increase to your attack.
When a red armourslayer fights a blue armoured unit. The multiplier goes from 1.48 to 1.19, your attack increase is only 19%.
Gem weapons:
Ruby, Emerald, Sapphire weapons increase your weapon triangle damage further or decrease it. It notes a 20% increase in damage in the weapon description.
If you have a weapon advantage with your gemmed weapon, it will increase your damage by 39% or 1.39 for the multiplier when you want to calculate it.
If you have a weapon disadvantage with your gemmed weapon, it will decrease your damage by 39% or 0.61 for the multiplier when you want to calculate it.
Same colour weapons are neutral again.
Weapons that give advantage over colourless foes:
I just tested it with Robin and it is not the same as having an effective weapon bonus.
It is the same as having a triangle weapon advantage.
So Robin, Cecilia and whoever else with their tomes that give a weapon advantage against colourless units gives an increase of 18% to their attack or 1.18 for the multiplier.
Staves:
Healers who use staves have a 29% damage decrease to their attack when entering combat.
That is approximately 0.71 for the multiplier when calculating it.