What does "SP" mean?  I may be daft but I cannot figure this out.

For example under Wear Armor on character sheet - the value is the sum of Base + STR + SP

the Sp. for the wear armor means Special, like bonuses you might gain from artifacts or other temporary buffs and such.

while the SP in initiative is in conjuncture with your weapons boxes, just so you can differentiate them more easily.

It's not very helpful as the book fails entirely to explain what 'SP' in weapon and initiative means. Anywhere else, it means the same as 'Spe' for special bonus (anything not covered by base/bonus). For weapons it just seems to be a marker - put a 1 in the SP box by the weapon and a 1 in the SP for initiative to mark that these are linked. It would have been simpler just to put initiative with each weapon, but I guess they wanted you to have the option of having more than one weapon linked to the same initiative column.

This of course presumes that your character never changes their armour, otherwise you need more initiative options per weapon (assuming your warrior isn't the type to wear full field plate in town).

I have no idea what the 'SP' in weapon/initiative is supposed to stand for.. anyone?

Under initiative the different slots are labeled as Sp1,Sp2, etc.  I recommend using the "SP" spot next to weapon to indicate which slot represents each initiative.  Youd think you'd just put the top one first but, as weapons change or for whatever reasons (in find the Anima sheet to be VERY well thought out) and this makes classing weapons together under the init column without having to individually reference each weapon (ie if all weapons except your dagger give you the same initive they will all be under "SP2" in init and write that in next to the weap where the dagger is "sp1" next to weap and in init

I understood it as "specialty", as the first box is for unarmed (adding the +20 bonus), the second and third one let you have some often used weapons having different initiative scores

oops quite misread the question, this is only for initiative, Spe can mean different things