I get the same output even after using
GraphPlot[Rule @@@ edges,
VertexCoordinates -> Thread[vertices -> crds],
EdgeRenderingFunction -> (With[{w =
Pick[Rescale[weights],
edges, (#2 | Reverse[#2])][[1]]}, {Thickness[.02 (.1 + w)],
ColorData["SunsetColors"][.9 w], Line[#1]}] &),
AspectRatio -> 1]