Since the weight matrix is actually the transpose of the weight matrix (sbromberger/SimpleWeightedGraphs.jl#65 (comment)), the wrong value is being read in the current implementation:
julia> s = SimpleWeightedDiGraph([1,2,1], [2,1,2], [1,1,1])
{2, 2} directed simple Int64 graph with Int64 weights
julia> get_weight(s,1,2)
2
Which is wrong because the weight of the Edge 1 => 2 is 1, not 2. This occurs because, get_weight is calling s.weights[2,1]. However, the weights field is not transposed.