Why is a pendulum with a bob of the same size but larger mass than another bob damped more lightly?

The heavier bob has more kinetic energy/potential energy/momentum for any given amplitude of the two pendulums due to its larger mass, as each of these three quantities depend linearly on mass. The damping is due to air resistance and seeing as the bobs are the same size, we must consider the energy (potential/kinetic). The heavier bob will lose a smaller percentage of its energy per oscillation so it is therefore less heavily damped than the lighter bob.
We can also visualise this through inertia, where inertia is the resistance an object has to a change in its state of motion. Since greater mass = greater inertia, the heavier bob will have greater opposition to something, air resistance in this case, changing its state of motion.