It's about range and wind and rpm. Light bullets do fine at ranges where wind isn't of great significance. 200 yards is reasonable 100-110 grain bullets in the 30s. But when you get to long range, you need a higher ballistic coefficient to prevent the wind blowing the bullet around so much. You also need it to minimize bullet drift from your group centers.
Because light bullets are going faster than heavy ones, for a given twist rate, they are spinning faster. This means the effects of any tiny bit of imbalance in the bullet mass are exaggerated. If a bullet from a 10 inch twist is going 3000 fps, a bullet with a 0.00025" off-axis center of gravity, it will drift laterally in away from the average trajectory at a speed of 2.83"/sec, opening groups at that rate. A heavier bullet going 2650 fps with that same amount of CG offset will drift a proportionally slower 2.50"/sec. At short range, this proportionality cancels out the difference because the faster bullet gets to the target sooner, causing the net group opening effect to be about the same for both. But as you shoot farther, assuming the bullets have the same ogive and tail profiles, the higher BC the heavier bullet's greater sectional density means it will lose speed more slowly. The lower BC light bullet will lose velocity faster, so the time of flight between each additional 100 yards grows faster for the light bullet, and with it, the amount of drift away from the mean point of impact.
