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If you want to combine the thickness with the color information, you could do this:

Plot[{1.1 Sin[x], .9 Sin[x]}, {x, 0, 3 Pi}, 
 PlotStyle -> {Thickness[0.01]}, ColorFunction -> "BlueGreenYellow", 
 Filling -> {1 -> {2}}]

Thanks Kuba for pointing out Artes' answer that shows how Filling can work here.