We consider message-efficient broadcast tolerating Byzantine faults in a multi-hop wireless sensor network. Assuming a grid network where all nodes have a communication range of $r$, and a single neighborhood contains at most $t$ dishonest and collision-capable (bad) nodes, each with a message budget $m_f$, we investigate the minimum message budget $m$ that each honest (good) node must have in order to achieve reliable broadcast. We consider three cases: (1) $m_f$ is known in advance and $m$ is homogeneous among all good nodes; (2) $m_f$ is known in advance and $m$ is heterogeneous among good nodes; (3) $m_f$ is unknown. For the first two cases, we present possibility results and broadcast protocols that have message costs within twice the lower bound. For the third case, we present a coding scheme that helps verify the integrity of messages at a receiving node without using any cryptographic techniques. This code leads to a {\em reactive local broadcast} primitive that has probabilistic reliability guarantees. Combined with a previously proposed scheme, it results in a broadcast protocol for $t < \frac 1{2} r(2r+1)$ that guarantees reliability with high probability.