Are lighter cars safer than heavier cars?

No, lighter cars are not safer. The size of a car matters if you are considering the safety of a car. The size and weight protect in many ways. In case of a car crash, the heavier car will push the lighter one backwards.

Heavier cars usually have more interior space, the more the interior space the less likely you are to get smashed in a car crash. Lighter car crash harder than a heavy car, as a result there is more effect of the crash on the occupants of the lighter car.