The extra force is mostly a problem for the tree, not for you. You get injured either because something squishes you (modern cars are good at avoiding that), or because you are decelerated too quickly, which is a function of speed and stopping distance.
With movable/deformable obstacles, heavier car = obstacle gets moved/deformed more = higher stopping distance.
A heavier car doesn't reduce stopping distance with heavier obstacles (a bigger car increases it though).
Your own weight has to decelerate to a stop, and the force it takes for your head to go 60 to 0 doesn't change based on what's around you. What does change its that a heavy car may resist the obstacle more -> longer distance until stop -> longer time to stop -> your head has more time to stop -> lower deceleration force on your head.
For whom? Heavier cars are safer because they slow down less when you hit something. If you hit something sturdy enough to stop you dead anyway you’ll probably cop a similar amount of damage as a smaller car.
