The general idea behind Luto's confusing comments is that the NPC isn't using the exact same thing that you gave them. Ultimately all that an NPC has, as far as weapon stats, is weapon *type* and upgrade number. (For example, mine is great katana, upgrade #7, whatever that ends up meaning. It is *not* Kiku-Ichimonji with 66 damage and 450 delay.) The game will calculate their effective damage/delay behind the scenes from there.
The point is that you should simply take it as "oh, time for a new NPC weapon upgrade since Luto said something about weapons". And also that when deciding between weapons, ignore anything that goes "well at this upgrade level, the GAX thing has the best DPS, followed by the GKT thing, and don't even touch that club it sucks" - because the NPC isn't using the actual weapon you're forking over. And therefore you shouldn't pick out which weapon is best based on the stats of the weapon you fork over.