Restaking protocols expand validator responsibilities beyond consensus, but their security depends on resistance to Sybil attacks. We introduce a formal framework for Sybil-proofness in restaking networks, distinguishing between two types of attacks, one in which other Sybil identities are kept out of an attack and one where multiple Sybil identities attack. We analyze marginal and multiplicative slashing mechanisms and characterize the conditions under which each deters Sybil strategies. We then prove an impossibility theorem: no slashing mechanism can simultaneously prevent both attack types. Finally, we study the impact of network structure through random graph models: while Erdös-Rényi networks remain Sybil-proof, even minimal heterogeneity in a two-block stochastic block model makes Sybil attacks profitable. These results reveal fundamental limits of mechanism design for restaking and highlight the critical role of network topology.