How do I add new weapon types?
Short answer: you can’t.
More complicated answer, but one that says “it’s kind of possible”:
The game only has space in its save memory to save weapon experience for 8 weapon types per unit. As such, adding a ninth weapon type with its weapon rank completely independent from the others would take a monumental ASM effort in restructuring the entire save data and modifying everything that checks for your weapon ranks. It might be more doable if you were willing to sacrifice another part of the save data, such as one of the support point slots, but would still take some ASM work to make the “check if you have the required rank” functions account for it. Alternative structures for associating WEXP to weapon ranks have been proposed that would theoretically enable more weapon types so long as no one unit has too many, but at the time of writing this none of those ideas have actually been implemented to my knowledge.
Making a new “weapon type” that doesn’t have ranks is easy, you just treat the item as something like dragonstone or monster weapon and use weapon locks to restrict it to certain units/classes.
But if you truly want to make a new weapon type with WEXP and ranks, you’ll either need to replace one of the existing types entirely, or make it share rank with one of the existing types. There are patches that let you redefine the weapon triangle on a per-type and/or per-item basis, so that’s not a concern.
With regard to replacing, the one big complication is that if you use SkillSys Strength/Magic Split, you’ll need to reconfigure it if you want to replace a magic weapon type with a physical weapon type, which means configuring and running a Custom Build.
Making two types share a rank, for example making daggers a subtype of swords, is probably the method with the least need to mess with ASM and Custom Build stuff, but involves some mildly tedious weapon lock management to restrict classes to one of the other – you’d have to apply a lock on all swords to only be usable by the intended sword-using classes, and likewise for all daggers. See here for a discussion of weapon locks.