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).