We formulate a local geometric criterion for weak cosmic censorship in black hole overcharging/overspinning thought experiments. Under the null convergence and generic conditions, matter injection turns a horizon cross section into a closed trapped surface. Any candidate final spacetime incompatible with this trapped surface is ruled out. The criterion excludes candidate final states locally described by superextremal Reissner-Nordstr"om, Kerr-Newman and Reissner-Nordstr"om-de Sitter geometries, as well as Weyl-class naked singularities, without using asymptotic charges or an extremal bound.