Upgrade to Babel 6

.eslintrc

{
  "parser": "babel-eslint",
  "env": {
    "es6": true,
    "mocha": true,
    "node": true
  },
  "ecmaFeatures": {
    "blockBindings": true,
    "forOf": true,
    "jsx": true,
    "modules": true
  },
  "rules": {
    "indent": [2, 2],
    "max-len": 0,
    "semi": 0,
    "quotes": 0,
    "semi": [2, "never"],
    "no-unused-vars": 2,
    "no-undef": 2,
    "no-console": 0,
    "no-trailing-spaces": 0,
    "curly": 0,
    "camelcase": 0,
    "react/jsx-boolean-value": 1,
    "jsx-quotes": 1,
    "react/jsx-no-undef": 1,
    "react/jsx-uses-react": 1,
    "react/jsx-uses-vars": 1,
    "react/no-did-mount-set-state": 0,
    "react/no-did-update-set-state": 1,
    "react/no-multi-comp": 1,
    "react/no-unknown-property": 1,
    "react/prop-types": 0,
    "react/react-in-jsx-scope": 0,
    "react/self-closing-comp": 1,
    "react/sort-comp": 1,
    "react/wrap-multilines": 1,
    "new-cap": [1, {"newIsCap": true, "capIsNew": false}],
  },
  "plugins": [
    "react"
  ]
}

modules.js

"devDependencies": {
  "babel-plugin-syntax-class-properties": "^6.0.14",
  "babel-preset-react": "^6.1.2",
  "eslint": "^1.9.0",
  "eslint-loader": "^1.1.1",
  "babel-core": "^6.1.2",
  "babel-loader": "^6.0.1",
  "babel-preset-es2015": "^6.1.2",
},

webpack.config.js

module.exports = {
  entry: {
    overview: './resources/assets/js/overview.jsx'
  },
  output: {
    path: __dirname + "/public/assets/js",
    filename: "[name].js"
  },
  module: {
    loaders: [
      {
        test: /\.jsx|.js$/,
        exclude: /node_modules/,
        loader: 'babel-loader',
        query: {
          plugins: ["syntax-class-properties"],
          presets: ["es2015", "react"]
        }
      },
      {
        test: /\.jsx|.js$/,
        exclude: /node_modules/,
        loader: 'eslint-loader'
      },
      {
        test: /\.json$/,
        exclude: /node_modules/,
        loader: 'json-loader'
      }
    ]
  },
  resolve: {
    extensions: ['', '.js', '.jsx']
  }
}