Теперь понятно.
Надо убрать nested из sizeData и elasticSizeScale (они у вас в единственном экземпляре, там nested не нужен. А вот с size все наоборот - там, как раз, nested необходим. Если это сделать то получится так:
DELETE test
PUT test
{
  "mappings": {
      "properties": {
        "sizeData": {
          "properties": {
            "elasticSizeScale": {
              "properties": {
                "id": {
                  "type": "long"
                },
                "name": {
                  "properties": {
                    "en": {
                      "type": "text",
                      "fields": {
                        "keyword": {
                          "type": "keyword",
                          "ignore_above": 256
                        }
                      }
                    },
                    "ru": {
                      "type": "text",
                      "fields": {
                        "keyword": {
                          "type": "keyword",
                          "ignore_above": 256
                        }
                      }
                    }
                  }
                },
                "sizes": {
                  "type": "nested",
                  "properties": {
                    "id": {
                      "type": "long"
                    },
                    "name": {
                      "properties": {
                        "en": {
                          "type": "text",
                          "fields": {
                            "keyword": {
                              "type": "keyword",
                              "ignore_above": 256
                            }
                          }
                        },
                        "ru": {
                          "type": "text",
                          "fields": {
                            "keyword": {
                              "type": "keyword",
                              "ignore_above": 256
                            }
                          }
                        }
                      }
                    },
                    "sizeOrder": {
                      "type": "long"
                    }
                  }
                }
              }
            },
            "id": {
              "type": "long"
            },
            "identifier": {
              "type": "text",
              "fields": {
                "keyword": {
                  "type": "keyword",
                  "ignore_above": 256
                }
              }
            },
            "name": {
              "properties": {
                "en": {
                  "type": "text",
                  "fields": {
                    "keyword": {
                      "type": "keyword",
                      "ignore_above": 256
                    }
                  }
                },
                "ru": {
                  "type": "text",
                  "fields": {
                    "keyword": {
                      "type": "keyword",
                      "ignore_above": 256
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
}
PUT test/_doc/1
{
  "sizeData": {
    "id": 1,
    "identifier": "group_size_shoes_mn",
    "name": {
      "ru": "Размер мужской обуви",
      "en": "Men's shoe sizes"
    },
    "elasticSizeScale": {
      "id": 3,
      "name": {
        "ru": "uk",
        "en": "uk"
      },
      "sizes": [
        {
          "id": 321,
          "name": {
            "ru": "6",
            "en": "6"
          },
          "sizeOrder": 2
        },
        {
          "id": 323,
          "name": {
            "ru": "7",
            "en": "7"
          },
          "sizeOrder": 4
        },
        {
          "id": 322,
          "name": {
            "ru": "6.5",
            "en": "6.5"
          },
          "sizeOrder": 3
        },
        {
          "id": 317,
          "name": {
            "ru": "13.5",
            "en": "13.5"
          },
          "sizeOrder": 17
        },
        {
          "id": 318,
          "name": {
            "ru": "14",
            "en": "14"
          },
          "sizeOrder": 18
        },
        {
          "id": 315,
          "name": {
            "ru": "12.5",
            "en": "12.5"
          },
          "sizeOrder": 15
        },
        {
          "id": 316,
          "name": {
            "ru": "13",
            "en": "13"
          },
          "sizeOrder": 16
        },
        {
          "id": 320,
          "name": {
            "ru": "5.5",
            "en": "5.5"
          },
          "sizeOrder": 1
        },
        {
          "id": 310,
          "name": {
            "ru": "10",
            "en": "10"
          },
          "sizeOrder": 10
        },
        {
          "id": 328,
          "name": {
            "ru": "9.5",
            "en": "9.5"
          },
          "sizeOrder": 9
        },
        {
          "id": 324,
          "name": {
            "ru": "7.5",
            "en": "7.5"
          },
          "sizeOrder": 5
        },
        {
          "id": 325,
          "name": {
            "ru": "8",
            "en": "8"
          },
          "sizeOrder": 6
        },
        {
          "id": 314,
          "name": {
            "ru": "12",
            "en": "12"
          },
          "sizeOrder": 14
        },
        {
          "id": 327,
          "name": {
            "ru": "9",
            "en": "9"
          },
          "sizeOrder": 8
        },
        {
          "id": 312,
          "name": {
            "ru": "11",
            "en": "11"
          },
          "sizeOrder": 12
        },
        {
          "id": 313,
          "name": {
            "ru": "11.5",
            "en": "11.5"
          },
          "sizeOrder": 13
        },
        {
          "id": 326,
          "name": {
            "ru": "8.5",
            "en": "8.5"
          },
          "sizeOrder": 7
        }
      ]
    }
  }
}
POST test/_search
{
  "size": 0,
  "aggs": {
    "by_size": {
      "nested": {
        "path": "sizeData.elasticSizeScale.sizes"
      },
      "aggs": {
        "by_id": {
          "terms": {
            "script": {
              "source": "doc['sizeData.elasticSizeScale.sizes.id'][0] + ' - ' + doc['sizeData.elasticSizeScale.sizes.name.ru.keyword'][0] + ' - ' + doc['sizeData.elasticSizeScale.sizes.sizeOrder'][0]"
            },
            "size": 10,
            "order": {
              "by_size": "asc"
            }
          },
          "aggs": {
            "by_size": {
              "max": {
                "field": "sizeData.elasticSizeScale.sizes.sizeOrder"
              }
            }
          }
        }
      }
    }
  }
}
В 7.12 мы добавили новую агрегацию, для таких случаев:
POST test/_search
{
  "size": 0,
  "aggs": {
    "by_size": {
      "nested": {
        "path": "sizeData.elasticSizeScale.sizes"
      },
      "aggs": {
        "by_id": {
          "multi_terms": {
            "terms": [{
              "field" : "sizeData.elasticSizeScale.sizes.id"
            }, {
              "field" : "sizeData.elasticSizeScale.sizes.name.ru.keyword"
            }, {
              "field" : "sizeData.elasticSizeScale.sizes.sizeOrder"
            }],
            "size": 10,
            "order": {
              "by_size": "asc"
            }
          },
          "aggs": {
            "by_size": {
              "max": {
                "field": "sizeData.elasticSizeScale.sizes.sizeOrder"
              }
            }
          }
        }
      }
    }
  }
}