it ABSOLUTELY does- the biggest difference any stat can make in the game- against enemies at or above your level.
So like, if you're fighting level 26 enemies, the difference in weapon damage if you're level 25 versus 26 is large, 24 versus 26 is huge, 23 vs 26 is massive, and if you're more than 3 levels below an enemy you won't be able to damage it at all.
This is why being level 29 at the least for the Hard raid is so important, and why being 30 still makes a big difference. However, you don't do any more damage to something 10 levels below you versus 4 levels below you, which is why can't just oneshot level 4 captains by shooting them in the leg.