Weary, annoy (3)
I believe the answer is:
irk
I believe this is a double definition.
'weary' is the first definition.
(thesaurus)
'annoy' is the second definition.
(I've seen this before)
(Other definitions for irk that I've seen before include "Severely annoy" , "Gall" , "Annoy, bother" , "Irritate, vex" , "English river" .)