A lightweight flywheel wil make the engine feel as if it had less low rpm torque, which in effect it will because there will be less kinetic energy 'stored' in the inertial mass of the rotating flywheel.
If you imagine an extreme hypothetical example of a flywheel with zero mass, then when taking off from rest all the power required to get the car's mass into motion must come from the power that the engine is producing at the moment the clutch engages, which won't be enough unless the rpm is substantially raised (increasing energy 'stored' in the engines rotational masses such as cranshaft), and / or the throttle opened significantly wider (to make more instantaneous power), and / or the clutch is slipped substantially.
Because you're revving the engine higher and / or opening the throttle wider, and dumping the clutch harder. The extra torque is coming from the engine being somewhat higher in the rpm range (where torque is higher), wider throttle opening, and from the kinetic energy embodied in the faster spinning rotational mass being higher due to the higher rpm. It's not because of a lighter flywheel...
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