It measures me a half of bitter (5)
I believe the answer is:
meter
'it measures' is the definition.
(I've seen this before)
'me a half of bitter' is the wordplay.
'a half of' means to take half the letters.
'bitter' halved is 'ter'.
'me'+'ter'='METER'
(Other definitions for meter that I've seen before include "Measuring device as for electricity consumption" , "Device that measures, say, electricity usage" , "Something measuring" , "Apparatus for measuring" , "Instrument for measuring quantity" .)