Well, they don't particularly NEED to add stats to the weapon (Though, it would help them scale), they really could do that.
Ironically, I believe the reasoning they gave for not putting stats on BLU's weapons was because they "Didn't want BLU's to have to farm dungeons for weapons"
Well, specifically: (Source)
So apparently, going to dungeons to get weapons (If you even bothered to do that given how fast BLU levels, you'd really able to get by on store bought stuff... If even that given that 1000 Needles AKA the only damaging skill worth anything levels 1-49 doesn't scale with stats at all) is "stressful" but farming Dungeons and EX Trials for the spells is apparently fine and dandy...Famitsu writer: Do we need to participate in content to collect weapons?
Yoshida: We designed it so you aren't forced to do so. Unlike other jobs, the BLU weapon doesn't have any stats on it. If it did have stats, you would end up going to dungeons over and over again. BLUs have restrictions to "queue with randoms", so it will just be stressful.
*Sigh*
Anyway, to fix BLU's damage... Make all their damage "Magical" with different elements in order to do Masked Carnival (Make their Physical damage skills just deal some form of Physical damage like Piercing or Slashing which, should only be the case for Drill Cannon? Mountain Buster should deal Earth damage, just like Titan-Egi)
Then nerf Off-Guard down to a more reasonable level of damage amp (Like 20%. Still more than other classes 10% damage boost, for the cost of only being single target because its a debuff rather than a self buff) and give them more reasonable potencies across the board. This should make it easier to balance them at all levels, so they're not utter trash while leveling up without using 1000 Needles, while also meaning they don't have some stupid scaling issues (Such as combo effects that triple the potency of a skill getting amped like crazy by the 50% boost from Maim and Mend and then the 50% boost from Off-Guard)