In gravity, spacelike separated regions can be dependent on each other due to the constraint equations. In my talk, I will propose a natural definition of subsystem independence and gravitational dressing of perturbations in classical gravity. Next, I show that extremal surfaces, generic trapped surfaces, and non-perturbative lumps of matter appear as features enabling subregion independence.  For extremal surfaces, the underlying reason is that localized perturbations on one side of the surface contribute negatively to the mass on the other side, making the gravitational constraints behave as if there exist both negative and positive charges. This suggests a simple intuitive picture for why extremal surfaces tend to separate independent subsystems.  It also supports the consistency of islands in massless gravity and provides hints on the nature of the split property in perturbatively quantized general relativity.  I also present new area bounds in de Sitter spacetimes that follow naturally from my analysis.