If you load up the same truck with more weight, keeping the same brakes, then it takes longer to stop. If there's the same braking force, energy to dissipate scales with mass.
It's a little bit more complex with an aircraft, as if it's heavier, it needs more lift, which means a different speed, height or attitude to fly level. More lift usually means more drag, both in approximate proportion to weight, and so more power is required to cruise heavier.
When losing energy descending though, if you try to shed speed deliberately with speedbrakes, that amount of braking isn't affected by weight, just by the speed and spoiler setting, and so a heavier aircraft will need more energy throwing away, and a longer deployment. The energy required to drop from 10,000m would make you travel at 440m/s in addition to your 300m/s cruise speed, so you need to lose a lot of energy on descent to land at 50m/s. That scales with mass, whereas the speedbraking force doesn't.