Colloidal gels are widely used in applications to modify the mechanical properties of fluids; in particular, they can provide yield stress, i.e. the ability to display solid-like properties at rest, while flowing upon application of a mechanical load. In this contribution we describe the yield behavior of a colloidal fiber network when it is subjected either to a macroscopic shear stress, or to a gravitational load obtained by inserting density-mismatched particles into the network. Delayed yielding is observed in both experiments. However, the time scales for the yielding process strongly differ from each other both on an absolute scale and in their dependence on the effective stress applied. We discuss how delayed yielding depends on background viscosity, intrinsic network relaxations, and on network porosity and elasticity