Weakness is a special Combat Stat for some Monsters that usually affects your Damage against them. Usually, weakness to a certain Weapon or Attack Style means that you will deal double damage when using it. This makes your attacks significantly more powerful, so it is generally recommended to use attacks against your opponents weakness whenever possible.
The Offhand Iron Dagger and Offhand Dagger+ add +1 or +3 Attack (or Maximum Hit) to increase the Damage against your opponent. If you are using an attack against your opponent's weakness, both Offhand Daggers added Attack stats will also be doubled. This doubling is calculated after the normal Damage calculations, with the added Attack bonuses, giving +2 or +6 to your Maximum Hit, and always dealing an even damage number.
The Giant Snake is weak to full Snakeskin Armour. Unlike other types of weakness, this does not affect your Damage to the Giant Snake, but rather affects its ability to damage you. Wearing less than full Snakeskin Armour will have no effect, but wearing full Snakeskin Armour will prevent the Giant Snake from dealing any damage to you at all, making the fight significantly easier.