Another KK - is it good?

Don't discount the possibility he is on AQ - re-raise PF to protect his Blind with a good hand... then the 1/2 pot bet to 'see' where he was. Your call rather than a re-raise could give him the information that you have like KQ or similar - probably suited - hence he feels he is in front and want s to drive you out before the river - and is not giving you draw odds...
Just a thought...
Could just as easily have AA or QQ - but that 1/2 pot bet mitigates against either .. especiallly QQ