I can understand your concern, I have been in these situations a lot. It seems like every hand the big stack plays, will be good for him because he seems to hit everytime, this is not the case! Of course they will hit it sometimes, like 33%, so you definitely have to give him credit sometimes, but when he gets out of line and is able to steal everypot, you should definitely play back at him. Play them cautiously and don't get out of line yourself, keep the pots small against them and be aggressive when you've got the nuts, or something good at least.
Those big bully's will never remain their stack if they really get out of line, just hope that they will make a mistake against you