A key introductory poem is signed Contraria Contrariis Vigilantius Dormitanus. This translates to Contrasting Opposites with opposites Wideawake : Sleepy head.
This is a direct reference to St Jerome. St Jerome was a religious satirist who had harsh anti-feminist views and was a staunch advocate of female virginity. His views were challenged by Vigilantius ( The wakefull one) St Jerome went on the offensive and wrote a treatise called Contra Vigilantius ( against Vigilantius) in this text St Jerome ironically attacked Vigilantius calling him Dormantius ( Sleepy one).
This is a real hint that the author of Avisa was doing exactly the same thing and was ironically attacking a woman by calling her the opposite of what she really was.
The book "praises " an incredibly chaste woman called Avisa but
When we read Willobies Avisa we realize that the woman who is intended to be the opposite of Avisa is Penelope.
So the book is really a hidden attack on an unchaste woman called Penelope.
In this instance the phrase may gather additional significance. Perhaps The author considers himself to be the wakeful (vigilant one) and considers H.W. to be the sleepy head (The Dreamer) and the full work is an attempt to make the dreamer H.W. wake up and realize the real truth about the woman that he is infatuated with