Two reasons by and large,
Firstly gust response (that is how much the aircraft is moved by turbulence) is a function of airspeed divided by wing loading. So a heavier aircraft, or one flying slower will suffer less grief in turbulence.
Secondly, if you're flying a 2-seat light aircraft, extra weight in the form of a passenger is Fwd of the centre of lift, so bringing the CG forwards. So the heavier aircraft is usually one with a more forward CG, which hence has more pitch stability.
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