If the stopper formnerly worked well but this seems to be a new development odds are the stopper is gummed up with hair and soap scum which prevents it from properly sealing.
I would suggest pulling the stopper out and cleaning it.
To pull the stopper out, remove the two screws that hold the overflow cover in place. You will see the wire control linkage attached to the back end of the lever on the inside of the cover. carefully pull up and out on the linkage and the stopper will lift right out.
I am including an illustration I prepared for snaking a tub drain. It will help you see how to remove the stopper.
