The lighter arrow will have a slightly higher initial velocity and fly farther...as long as the shape/build of each arrow is exactly the same. This is a simple "projectile motion" problem if we can remember back to our first course in Physics. Keeping it simple, the arrow does not accelerate or decelerate horizontally once it leaves the string. Vertically, it accelerates in the negative direction at a rate of 32.2 ft/sec^2(gravitational force). This will determine how long the arrows stay in flight, regardless of weight. If both arrows left the string at the same velocity, they would stay in flight for the exact same length of time. This isn't the case here though, as the arrows vary in weight...different velocities leaving the string. Thus, the arrow with the higher initial velocity (the lighter arrow) will fly farther than the heavier one of equal shape/build.
Brian