Recursive sum leaf nodes values bottom up to parrent node.

sumLeafNodesValues.js

var dumpHead = {
  label: "root",
  value: 0,
  children: [
    {
      label: "a",
      value: 0,
      children: [
        {
          label: "a-2-1",
          value: 0,
          children: [
            {
              label: "a-3-1",
              value: 3
            }
          ]
        },
        {
          label: "a-2-2",
          value: 0,
          children: [
            {
              label: "a-3-2",
              value: 2
            },
            {
              label: "a-3-3",
              value: 3
            },
            {
              label: "a-3-4",
              value: 10
            }
          ]
        }
      ]
    },
    {
      label: "b",
      value: 0,
      children: [
        {
          label: "b-2-1",
          value: 0,
          children: [
            {
              label: "b-3-1",
              value: 5
            }
          ]
        },
        {
          label: "b-2-2",
          value: 0,
          children: [
            {
              label: "b-3-2",
              value: 2
            },
            {
              label: "b-3-3",
              value: 4
            }
          ]
        }
      ]
    },
    {
      label: "c",
      value: 0,
      children: [
        {
          label: "c-2-1",
          value: 0,
          children: [
            {
              label: "c-3-1",
              value: 8
            }
          ]
        },
        {
          label: "c-2-2",
          value: 0,
          children: [
            {
              label: "c-3-2",
              value: 9
            },
            {
              label: "c-3-3",
              value: 10
            }
          ]
        }
      ]
    }
  ]
};

function traverse(node) {
  if (node.children === undefined) return node.value;
  var total = 0;
  for (var i = 0; i != node.children.length; ++i) {
    total += traverse(node.children[i]);
  }
  node.value = total;
  return node.value;
}

traverse(dumpHead);

console.log(JSON.stringify(dumpHead, null, 2));