  Let p > 2 be prime. We prove the weight part of Serre's conjecture for rank
two unitary groups for mod p representations in the unramified case (that is,
the Buzzard-Diamond-Jarvis conjecture for unitary groups), by proving that any
Serre weight which occurs is a predicted weight. This completes the analysis
begun in [BLGG11], which proved that all predicted Serre weights occur. Our
methods are purely local, using the theory of (phi,Ghat)-modules to determine
the possible reductions of certain two-dimensional crystalline representations.
