The link between Zeno behavior and homogeneity in hybrid systems is pursued. Zeno behavior is associated with homogeneous hybrid systems having negative degree. Zeno behavior is typically ruled out in homogeneous hybrid systems with nonnegative degree. Next, asymptotic stability in homogeneous systems is shown to be robust to homogeneous perturbations. In turn, homogeneous perturbations are used to characterize local, approximate homogeneity. For systems that are locally, approximately homogeneous with negative (respectively, nonnegative) degree, Zeno behavior can be established (respectively, ruled out typically). In addition, stability results based on linear and conical approximations are established.