grammar - Usage and meaning : 寝ろ vs 寝てろ?

I am on page 32, Ch.82 of よつばと！ Source : http://raw.senmanga.com/Yotsubato!/82/32

My translation of the highlighted text bubble is,

Now, sleep quietly okay.

But I am confused as to why 寝てろ is used here as opposed to 寝ろ ? Is it because sleep is a resultant state (something like 知っています or けっこんしています) ?

After some probing I came across this but it doesn't answer the difference between usage of 〜てろ and 〜ろform.

What I did come to know is, 寝てろ is a compact form of 寝ていろ which is imperative/command form of 寝ている. All in all, 寝ていろ is something like a command to sleep (or be in state of sleep or keep sleeping ?). why is the progressive form used here ? What kind of subtlety does it add ?

Answer

This type of いる is called a subsidiary verb, and what it means roughly depends on the context and the verb type. For details, see: When is Vている the continuation of action and when is it the continuation of state?

寝る is an ordinary action verb like 食べる, 走る or 勉強する. It's not an "instant state-change (aka punctual)" verb like 知る, 結婚する or 倒れる. This means when 寝て (the te-form of 寝る) is followed by いろ (the imperative form of いる), it usually means the continuation of the action (i.e., "be ～ing"). So 寝ていろ means "Be sleeping" or "Keep sleeping", while 寝ろ just means "Sleep." or "Go to bed."