Power is work done divided by time taken. If you raise 15 Kg the height of 100 feet in the same time as someone raising 10 Kg the same 100 feet, the former is working at a faster rate, even though the time is the same. The former is doing 50% more work than the latter and to do it in the same time requires the former to develop 50% more power.
Obviously that power is transmitted to the wheels and cadence is one way of doing it. Another way is to push harder. Most people find a balance between the two, using the gears appropriate to their strength. Too high a gear and you can't push hard enough and cadence drops. Too low a gear and, even with a high cadence, you may not transmit the power at a fast enough rate.