Learn English – What’s that supposed to mean vs what does that suppose to mean vs what’s that suppose to mean

There's no contradiction. In this sentence, positively doesn't have its literal meaning of "in a positive manner". Instead, it's used as an intensifier, emphasizing the following adjective ill.

When an English word is used as an intensifier, it loses its literal meaning. Originally, very meant "truly" (like verity, verify, verily, and so on), but now we can say very tasty ("tasty to a great degree"). Likewise, really meant "in reality", but now we can say really sick ("sick to a great degree").

A lot of similar words belong to this class, including awfully, absolutely, terribly, or the slang words super, way, totally, and literally.

You could replace the word 'peer' with 'look'

"Look down"

From the Cambridge dictionary -

Peer - "to look carefully or with difficulty"

https://dictionary.cambridge.org/dictionary/english/peer