Bowman aren't necessarily weak. It's just that their damage is very unstable until they have bow/crossbow mastery in the second job advancement. They also must deal with knocking back enemies when they get too close until getting power knockback in the second job advancement. This means that the early levels tend to be very difficult compared to the other classes.
It may seem that sins get a better deal in terms of long ranged attacks but they have to rely on lucky seven to do this damage. Bowman on the other hand do not have to continuosly use a skill to fight effectively. The skills are really situational in nature. Arrow bomb is used to stun enemies and then eliminate them with a volley of arrows. Power knockback is for when enemies get too close. This does not mean that you can't just spam skills until all the enemies are dead. My point is that bowmen don't have to use their skills continuously unlike sins.