We study the problem of distributed Kalman filtering, where a set of nodes are required to collectively estimate the state of a linear dynamic system from their measurements. In diffusion Kalman filtering strategies, neighboring state estimates are linearly combined using a set of scalar weights. In this work we show how to optimally select the weights, and propose an adaptive algorithm to adapt them using local information at every node. The algorithm is fully distributed and runs in real time, with low processing complexity. Our simulation results show performance improvement in comparison to the case where fixed, non-adaptive weights are used.