You can find the damage interval you can do with a weapon in the detailed information window of a weapon, in the example image it is the fourth field from below. The damage interval is determined by your skills. For weapons without a Skill increase bonus (SIB), the start of the interval is determined by your damage profession level. The exact relation is:

Start of damage interval = 25% + 25% * Profession level

The resulting percentage is with respect to the maximal damage the weapon can do. The end of the interval is always the maximal damage, so 100%.
For a SIB weapon, the damage interval is 25% to 50% when you are not in yet in the learning period. When you start the learning period, the damage interval jumps to 40% to 80%, and will linearly increase until 50% to 100%. At this point the learning period is over, and the weapon is maxed.