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}}]

![thickness][1]

Thanks Kuba for pointing out [Artes' answer](http://mathematica.stackexchange.com/a/5124/245) that shows how `Filling` can work here.

**Edit**

In response to the comment, let me suggest something **completely different**: do the whole thing in *three dimensions*, and use the fact that one can draw 3D lines as [`Tube`](http://reference.wolfram.com/mathematica/ref/Tube.html) which allows the specification of a varying radius at each intermediate point along the line. Here, the calculation of the perpendicular directions to the curve is already done for us:

    makeTube[p_, width_: .1, color_: Darker[Blue]] := 
     Graphics3D[{color, 
         Tube[#, width Abs[#[[All, 2]]]] &@
          First[Map[Append[#, 0] &, 
            First@Cases[Normal[#], _Line, Infinity], {2}]]}, 
        Boxed -> False, Axes -> {True, True, False}, 
        AxesOrigin -> {0, 0, 0}, ViewPoint -> {0, 0, 10000}, 
        ViewVertical -> {0, 1, 0}, Lighting -> "Neutral"] &[p]
    
    makeTube[Plot[Sin[x], {x, 0, 3 Pi}]]

![3d plot][2]

As a `Graphics3D` object, this by default has `AspectRatio -> Automatic`, which is needed to avoid distortion of the thickness. 

Here, I've chosen the `ViewPoint` and `ViewVertical` to make the result look like a 2D plot. This may be cheating, but maybe you can use the idea if at some point you want to  include a third dimension... 

The function `makeTube` assumes that the argument `p` contains a `Line` as it would be generated by the standard `Plot` command. One could add more logic to analyze `p`, in case it contains more than one `Line`, etc. But this is just a proof of principle.

  [1]: https://i.sstatic.net/hgNKo.png
  [2]: https://i.sstatic.net/XnsXB.png