He loves her dearly (not half!) – could be so in love? (4,4,5)
I believe the answer is:
head over heels
'so in love?' is the definition.
(informal phrase meaning very much in love)
'he loves her dearly not half could be' is the wordplay.
'not half' indicates taking half.
'could be' indicates an anagram.
'dearly' cut in half is 'dea'.
'loves'+'her'+'dea'='lovesherdea'
'lovesherdea' anagrammed gives 'adoverheels'.
'he'+'adoverheels'='HEAD OVER HEELS'
(Other definitions for head over heels that I've seen before include "Completely - turning as in a somersault" , "In great confusion (because of love?)" , "In disorderly haste" , "topsy-turvy" , "(In relation to love) madly" .)