Graduate gets weight to stick (5)
I believe the answer is:
baton
'to stick' is the definition.
(term for a stick or staff)
'graduate gets weight' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'gets' says to put letters next to each other.
'weight' becomes 'ton' (unit of weight).
'ba'+'ton'='BATON'
(Other definitions for baton that I've seen before include "Relay race stick" , "Staff" , "A stick for a conductor and policeman" , "Light wand" , "weapon" .)