We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations in quantum field theory force generalized symmetries to appear in dual pairs. Verifying this prediction helps us find the full set of nontrivial conserved charges-associated, in equal parts, with 2-form and (D-2)-form currents. Their total number is D(D+1). We compute the quantum commutators of pairs of dual charges, showing that they are nonvanishing for regions whose boundaries are nontrivially linked with each other and zero otherwise, as expected on general grounds. We also consider general linearized higher-curvature gravities. These propagate, in addition to the usual graviton, a spin-0 mode as well as a massive ghostlike spin-2 mode. When the latter is absent, the theory is unitary and the dual-pairs principle is respected. In particular, we find that the number and types of charges remain the same as for Einstein gravity, and that they correspond to continuous generalizations of the Einsteinian ones.