Both size and weight affect the forces people inside a vehicle experience during a crash. The magnitude of those forces is directly related to the risk of injury.
In larger-sized vehicles, the longer distance from the front of the vehicle to the occupant compartment provides more protection in frontal crashes, which account for more than half of passenger vehicle occupant deaths. The longer that distance, the more the frame of the vehicle can be crushed before it crushes the people inside.
Weight is important when two vehicles collide. The bigger vehicle will push the lighter one backward during the impact. That puts less force on the people inside the heavier vehicle and more on the people in the lighter vehicle.
IIHS demonstrated the role of size and weight in a series of crash tests in 2019, pairing a midsize SUV and small car made by Kia and a large car and minicar made by Toyota in collisions with each other. Both of the smaller vehicles, the 2018 Kia Forte and 2018 Toyota Yaris iA, had good ratings in the five IIHS tests relevant to driver protection, but they performed poorly in collisions with the larger vehicles.
Improvements in crash protection have made vehicles of all sizes safer, but bigger vehicles are still safer than smaller ones even with those improvements. As the chart below illustrates, crash deaths decline as vehicle size increases. A similar chart using weight instead of size would look almost the same.
More on driver death rates by vehicle type and size