A strangely weak point to open one's eyes (6)
I believe the answer is:
awaken
'open one's eyes' is the definition.
(I've seen this in another clue)
'a strangely weak point' is the wordplay.
'strangely' indicates anagramming the letters.
'point' becomes 'n' (North).
'weak' with letters rearranged gives 'wake'.
'a'+'wake'+'n'='AWAKEN'
'to' acts as a link.
(Other definitions for awaken that I've seen before include "Rouse from sleep" , "Call forth" , "Cause to remember" , "Emerge from sleep" , "Stir" .)