Playing a hand vs a bully

In the Paradise Masters $200 Rebuys, I played an interesting hand versus a bully. Before this hand, I raised to 200 (blinds 25-50) in EP with TT, he reraised in MP to 600, folded to me and I called. Flop came K32, I had like a 6k stack, and decided to lead here for 950, he didn't cooperate and raised to 2700, so I gave him credit and folded. Probably he had a hand like AK, AA, or probably he was just a bully who likes to take control of the hand and made me fold. Well, with this information, later I opened in MP with AA and a 5k+ stack, blinds were 50-100 and I raised to 350 in MP, same bully with a 20k stack called in LP. Flop came Ks7c3d, excellent flop for my hand, so I checked since I knew he couldn't help to bet, he didn't disappoint and bet 600, I raised, of course, and I was almost certain he would reraise me there, bullies can't help it, I raised to 1500 and again he didn't disappoint and reraised to 2600 or so; now I went all in for 3k more, if he has a set, so be it, but he folded, since he couldn't reraise me out the hand anymore. Now he could have been a donkey bully or a smart bully; a donkey bully when with a stack, it's gonna be raising you any time he feels like it, no matter what, and he could have anything, and if he had anything at all he's calling you in the previous spot. A smart bully is gonna reraise you to take control of the hand, but in the previous spot, he's capable of folding hands like KQ, because of the strength I showed; I don't know if he was a donkey and had something like T8 in that hand, or if he was a smart player and he had KQ; but the beauty of the analysis it's that it doesn't matter, and the best play was to just call after his reraise. By going all in, I failed to gain some more chips there. Lets see, if he's the smart one and I just call, it's gonna be hard for him to fold the KQ in the turn or river, and most probably he's betting again in the turn if I check; if he's the donkey, he's betting for sure the turn, no matter what. So, on both cases I win more chips. Of course once in a while he'll have something like 54 and could catch a 6, or KJ and catch the J; but I think the risk was worth it. When with a hand, give the bully all the chances you can to let him bet into you; sometimes by checking, sometimes by betting "scared", and sometimes by check-raising small; it depends of the size of your stack the pressure you'll need to apply to get full value of your hand, let him make the last bet. More often than not, his chips will be flying in your direction.