I'm using an Axe leveled up to plus 3,think it's 110 strength or whatever (yet another that isn't explained - weapon stats, what are all those numbers? The game doesn't say)
Weapon upgrade level is paramount, even more important than your character level. Upgrade that weapon to +5 for starters.
Weapon damage works like this - It has a base damage amount which increases as you upgrade the weapon. Then you get extra
bonus damage from your stats. Leveling up your character will increase this bonus damage amount, so long as you are leveling up the corresponding stats to which the weapon you are using gains bonus damage from.
This bonus damage scales on a letter grading S being best then A to E, E being worst. The letter grading does increase as you upgrade the weapon, so don't worry about a C so much, but an E is always going to kind of suck comparatively.
Example below:
So this weapon is a fully upgraded (15+) Bastard Sword (can buy it from Andre iirc).
It does 262 [GREEN box above] Physical Damage and scales a C with Strength and a C with Dexterity [RED] (commonly referred to as a quality weapon, a phrase borrowed from Demon's Souls). The bonus damage this person gets when using this weapon is an additional 273 [YELLOW] damage. So they have obviously been leveling up their STR and DEX to have that amount of bonus damage. In total that's 536 physical damage [BLUE].
The other numbers
Magic, Fire, Lightning are all for weapons upgraded along those upgrade paths - as you progress through the game there are various embers that let you upgrade your weapon in different ways. The damage done when upgraded this way is split between physical damage and the particular element. So when you upgrade say a weapon to become a fire weapon, it might do 200 physical damage normally, but upgraded to a fire weapon it might do 100 phys and 100 fire - same total BUT..... Cool if your enemy is weak to fire, sucks if it's resistant because you might only be doing say 100 damage instead of a full 200, which depends on the individual enemies resistance stats to that particular damage type. For example the boss Quelaag is 100% resistant to fire, so with a fire weapon you would only be doing the 100 phys damage, all your 100 fire damage would be wasted.
Elemental upgrades (Fire, Lightning)
REMOVES stat scaling, so that C/C above will be removed and there will be no bonus damage regardless of your stats.
Magic (Magic, Divine etc) weapons change to include scaling from the Intelligence or Faith stats respectively, and this is for sorcery or miracle users leveling up INT or FTH and can be ignored if you're not using magic.
Critical is the extra damage you do when doing a critical attack (riposte or backstab)
ParamBonus - The letter grading and which stat the weapon receives bonus damage from. Left to Right: Strength, Dexterity, Intelligence, Faith.
Aux Effects - Bleed, Poison, Divine, Occult. Some weapons cause bleed or poison to build up, some enemies are particularly weak to occult or divine weapons.
[Middle column]
DmgReduction% - This is the defense stats when the weapon is two-handed and used to BLOCK attacks. In the above, the Bastard Sword absorbs 60% of physical damage when used to block an attack, so not as good as a shield, but better than nothing. Magic 10%, Fire 40% and so on.
This is the column you want to especially look at when looking at a shield's stats.
Stability - is the rating of how much stamina is lost when blocking an attack. The higher this number the better because high stability = less stamina lost from blocking. When you are out of stamina you can't roll, run or swing your weapon and if you block an attack and it reduces more stamina than you have left, you become guard broken and temporarily stunned, not good.
ReqParam - Stats required to use the weapon. Bastard Sword is 16 STR, 10 DEX. If you two-hand weapons, they require less STR, two-handed swings take more stamina but do more damage.
Durability - using the weapon very slowly lowers this, repair at a blacksmith or buy the repair box to repair at any bonfire, it costs a few souls to repair.
Weight - Your weapons and armour all have weight which effects your movement speed with tiers at below 25% maximum equipment load (fastest run and roll), up to 50% (mid), up to 100% (slow or 'fat' roll) and over 100% you can't run or roll. Leveling up Endurance increases your total equipment load, as do a couple of rings and a headpiece found in the game when you wear them.
Right-hand column - Can be switched between your stats or the totals shown above.