That's the problem: Weapons are blocked from using some of the enchants apparel can(and that perks can, for that matter). The drop down menu for weapon enchants doesn't include the StealthBoyInvis effect, as the OP described. See pic for what happens when you switch an apparel enchant with stealth to a weapon enchant. I'd love for someone more experienced to demonstrate otherwise, but my tomfoolery with scripting and hidden perks seems to be the simplest way to make the game behave as if the weapon is cloaking the player.