MetaPost: Randomly variably thick curves

While not an answer the question of variably thick curves, another approach to emulate the desired outcome is to think of the curves as simply two offset sine waves, connected at each end:

  color base_colour;
  base_colour := \MPcolor{BaseColour};

  deviation_dark := uniformdeviate( .025 );
  def dark_colour = deviation_dark [base_colour, black] enddef;

  wave_height := 1.5mm;

  path top_wave;
  top_wave := (0, 0);

  wave_resolution := 20;

  for x = 0 step (1 / wave_resolution) until 2:
    y := sin( x * pi );
    top_wave := top_wave .. (x, y);

  % Duplicate the top wave, but move it up a random amount.
  path bottom_wave;
  bottom_wave := top_wave shifted( 0, wave_height );

  % Offset the waves.
  top_wave := top_wave xyscaled (5.5cm, 5mm);
  bottom_wave := bottom_wave xyscaled (6.5cm, 4.5mm);

  % Create a path for connecting the waves.
  path wave_right_side;
  wave_right_side :=
    (point length(top_wave) of top_wave) --
    (point length(bottom_wave) of bottom_wave);

  % Connect the waves.
  path wave;
  wave := top_wave & wave_right_side & reverse bottom_wave -- cycle;

  % Stretch the wave to extend beyond the page boundaries.
  wave := wave xscaled( 2.5 );

  draw wave withpen pencircle scaled 3mm withcolor .7[base_colour,white];
  fill wave withcolor dark_colour;

This produces a reasonable facsimile:

Double Sine Wave

If there's no obvious way of doing it easily, it's almost always possible to implement missing features. Solution to this problem i came up with was basically: to write a function that generates an offset path to a given path at distance, that is a function of a time on a given path; to generate two such paths at both sides of a given path; connect them; fill the resulting shape. The code (which is a part of a library and, unfortunately, quite long and messy to cite here) you can find here. Once you include this library (input, you can write code like this:

path p;
p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0);
draw brush (p)(1cm*sin(offsetPathLength*pi)) withcolor (0.75, 0.75, 1);
draw brush (p)(0.6cm*sin(offsetPathLength*pi)) withcolor (0.5, 0.5, 1);

where function "brush", which actually draws variable width line, has two arguments: first is a path; and second is some arbitrary function of either "offsetPathLength", which is an arclength on a path, or "offsetPathTime", which is a time on a path; and get picture like this: enter image description here

To get more detail you might need to subdivide original path. It seems to work with ConTeXt, but might require some tweaking.