Weight does't automatically imply safety. If I take a Yaris and put 1000lbs of dumbbells in the trunk, it doesn't magically become safer because it has higher weight. Cars are not solid rigid bodies. Conservation of momentum applies when 2 rigid bodies collide. If
@Giannis is around he can probably educate us more on finite element analysis that would be required when 2 non-rigid bodies collide.
Going back to weight, yes, if the weight is used to make the structure stronger, sure it will be safer. But if a car is heavier because it's engine or transmission is heavier, it is not going to be any safer. Also if structure is made of a material with higher specific strength, it can be both lighter and safer, case in point carbon fibre.