I tried to do the same thing inside postman, but without luck.
This is my get request inside postman
{{base_url}}/directory_items.json?period=weekly&order=likes_received&_=1542354108586&api_key={{api_key}}&api_username={{api_username}}.
It could possibly be your api_key and api_username since you probably don’t actually have one for meta. You can leave it off on this site since it is a public endpoint. You can also leave off the &_=1542354108586 part since that is just used by the browser and not needed for regular api calls.
Here is the curl command I used:
curl -i -sS -X GET "https://meta.discourse.org/directory_items.json?period=weekly&order=likes_received"