Here parameters of API respond :
{\"cod\":\"200\",\"message\":0.0045, \"city\":{\"id\":1851632,\"name\":\"Shuzenji\", \"coord\":{\"lon\":138.933334,\"lat\":34.96
It looks like 'weather' is an array.
Try $data['list'][0]['weather'][0]['description'];
$data['list'][0]['weather'][0]['description'];