Sorry to join this thread so late but as they say better l;ate than never.
Here is a hand from a HU NL cash game.
Villain is a good aggressive player, 50 hands ago Villain got lucky and busted the Hero's with . Villain keeps on consistently raising OOP with a various range of hands.
Blinds £10/£20
Hero OTB has £3264
Villain has £4233
Hero is dealt

Villain raises to £60
Hero raises to £180
Villain calls
Flop:

Villain checks
What now...?
Pretty starightforward so fa...Villain raised and as a perceived aggressive player you reraised him to make him fold pre flop and he does not oblige by folding and calls your reraise instead.
I am inclined to think that Villain has at least a playable hand at this point as he has called your reraise but he is still getting decent enough implied odds of around 17/1 if he flops great anyway.
On the flop however he has checked to you and you have hit middle pair and a back door flush draw so I feel it is important to bet here. SOmewhere in the region of half the pot to 3/4 of the pot seems reasonable as you have a good chance of being in front and there has to be a good chance that Villain will fold as he will feel you have at least a pair or two big overcards as at face value neither of you really should have been helped byt he flop considering the pre flop action.
(BTW One thing you haven't mentioned is how Villain perceives you but as you mentioned that he cracked your AA with a KK earlier I assume he thinks you are a tight player or one that only plays premium hands. As such it would put greater emphasis on him having a playable hand pre flop after your reraise).
Villains check call on the flop doesn't tell you a great deal, however, as he could be on a draw such as holding two overcards in diamonds but surely with this type of hand he may have preferred to lead into you or check raise you on the flop. After all he is described as aggressive and with two overs he may even figure he is a fasvourite over you and want to commit chips at this point. Then again he may have a set of 2's or 9's and may have decided that he wants to see no diamond come off before getting chips comitted. Having said that when in a heads up type situation it's less likely that you are afraid of a flush type draw in the same way you would if it was a multi contested flop. Whatever the case you cannot really be that happy about his call but on to the turn you go and you still may have the best hand although I don't feel at this point he has two overcards unless it is a big overpair.
OK, on to the turn...Hero bets £300
Villain calls £300
There is £960 in the pot
The turn card is the

So the flop is:

The
Villain checks
...Hero bets £850 making the pot £1810 and leaving himself £1934
Villain checks again and this is like a godsend imo as he has now shown definite weakness (two consecutive checks) and the turn card has given you lots of additional outs if you are checkraised and you could still easily be in front.
Making your pot sized bet makes sure that Villain cannot call you with a draw but he throws a major spanner in the works by check raising you all in so now you have to make some decisions.
Villain raises all in for £3753
Do you Call or Fold?
The pot is now 3734 and it will cost you your remaining 1934 to call which is roughly 2/1.
Firstly this is a cash NL game and I cannot believe for the life of me you can fold here and believe you must make a mandatory call.
To fold you have to be confident that you are going to lose 67% of the time from this position and even though you may have tainted outs some of them surely are clean ones.
Currently you figure you have 9 clubs plus 3 x Fives and 3 x Tens and possibly 2 x sixes and 2 x sevens but even if you discount on average 4 of them (which I believe is fair) you are going to expect to have 15 outs that win for you assuming that you are behind at this point and need to catch up which is roughly 33% chance of winning. You have to also calculate whether your opponent (who is very aggressive) is the type of player who likes to commit chips with a draw on the turn or capable of making a complete bluff at this pot in this spot not to mention allow for your already being in front with the pair of 6's.
Well thats my perspective on this hand anyway but for me I am committing to this pot with my bet on the turn and him check raising whilst not welcomed is not going to stop me from calling. Whilst I prefer to do the original pushing of chips into the pot I figure that nearly all of my perceived outs are good as Villain most likely has an overpair and the only real hand I don't want him to have is a set of 2's or 9's or even 8's on the turn but if he has so be it. I can't go running scared just because there's a lot of money in the pot.