It was adding User-Agent and removing Authorization, but only when
existing headers had the exact right casing. Node uses caseless logic
when managing headers.

This was causing some requests to have `User-Agent` appended to the
headers object and overriding provided agent strings.

Also included is an update to not override the `Content-Length` if it
was already defined in the options. It can be desirable to manually
specify a content length that does not match the data on hand.
Especially for testing.

Play nice with axios#3703

…checking-http-adapter