I understand that you have two goals in mind. First of all, you should decide which unit length to use for managing heights. I have chosen inches, but you could work with feet if you need. This will simplify the scenario and will allow you to work easily with the data, but you could always create a function that translates inches to the foot/inches combo in order to show the data to a third party. This is the example table that I will use:

And this is my code, I will explain it at the bottom:

function main() {
  var sheet = SpreadsheetApp.getActiveSheet();
  var data = sheet.getDataRange().getValues();

  data = sortTable(data);
  sheet.getDataRange().setValues(data);

  for (var i = 1; i < data.length; i++) {
    data[i][2] = gradient(data.length, i);
  }

  for (var i = 1; i < data.length; i++) {
    sheet.getRange(i, 2).setBackground("#" + data[i][2][0] + data[i][2][1] +
      data[i][2][2]);
  }
}

function sortTable(data) {
  data.sort(function(a, b) {
    return b[1] - a[1];
  })

  return data;
}

function gradient(arraySize, position) {
  var relativePosition = position / arraySize;
  var topColor = [parseInt("00", 16), parseInt("7A", 16), parseInt("33",
    16)]; // Green
  var bottomColor = [parseInt("FF", 16), parseInt("FF", 16), parseInt("FF",
    16)]; // White
  var positionColor = [0, 0, 0];

  for (var i = 0; i < 3; i++) {
    positionColor[i] = Math.floor(topColor[i] * (1 - relativePosition) +
      bottomColor[i] * relativePosition).toString(16);
  }

  return positionColor;
}

First of all you have to read the data with a combination of getValues()/setValues(), and once you do that you can sort the table based on height so you can create the gradient later. Please notice how I separated the sorting function for better clarity.

After that you need the gradient color for setBackground(). To do so I developed a simple linear gradient function that calculates the RGB code from the top to the bottom. In my example the gradient fades from green to white, but you can change it. I also separated the gradient script into its own function. At this point you already have the sorted table and its gradient colors, so you only have to use setValues() and you are done. Feel free to leave any comment if you have doubts about this approach. This would be the final result:

UPDATE

Based in your comments I get that you need an imperial height format. For that case, you could use =INT(B2)&"' "&TRIM(TEXT(ROUND(MOD(B2,1)*12*16,0)/16,"# ??/??")&"""") (assuming that B2 contains the height). This approach will use Sheets Formulas to calculate the remainder part of the height, and its expression as an irreducible fraction. This is the final result: