The purpose of the flywheel is to store and supply kinetic energy to the engine to enable it to rotate during the periods, when the engine is not producing energy.
In a two stroke engine, firing takes place every revolution, whereas in a four stroke engine, firing takes place every alternate revolution. In two stroke engine, the eigine generates energy for approximately 180 degrees of rotation of therankshaft and therefore needs energy from the flywheel for the remaining 180 degrees before the engine fires again. In a four stroke engine,the engine generates energy for 180 degrees of crankshaft rotation and therefore needs energy from the flywheel for the remaining 270 degrees of crankshaft rotation.
From this it is seen that the energy storage requirement in a four stroke engine is higher. Therefore the flywheels used in four stroke engines are heavier. To be precise, the flywheel should have a higher moment of inertia about its axis of rotation rather than just be heavier .
The difference is not very much higher as the energy requirement during exhaust and suction strokes are small compared to the energy requirement during the compression stroke.