We show that the equilibrium connected correlation of the two-body loss rate provides access to the dynamical bulk viscosity in weakly dissipative quantum gases. Starting from the Lindblad equation for weak inelastic losses, we derive the loss-current operator and, using a counting-field formulation of the loss statistics, the relation between the statistics of detected losses and the equilibrium loss-rate correlator. The connected correlation of the two-body loss rate is found to be proportional to the equilibrium contact correlation and hence to the bulk-viscosity spectrum. We show that the measured loss-counting covariance contains, besides the Poissonian self-correlation, a quantum-jump backaction term of the same order as the target correlator, which is fixed by the transient of the mean loss rate after the loss is switched on. The bulk-viscosity spectrum can therefore be reconstructed from the combination of the loss-counting covariance and the mean loss dynamics. Our result identifies weak two-body loss dynamics as a probe of dynamical bulk viscosity, whose measurement has remained elusive in experiments.