first of all i didnt mean to offend you by stating that check calling is a weak move.i just analyz the play IMO.
back to the second hand though.
pot is 4k and you at this stage have abt 3k left and i think villan has abut 8k or there abouts.
you say you wanna double up so your just calling his bets.
you also say that you actually dont think he has an A.
the thing is flop can fit many hands that would call your preflop raise ,with A T and two hearts in it.
i think the pot at this stage is big enough for you to wanna take it home.
if he is bluffing and has nothing,he can see that your pot commited so he is not gonna make any more bluff attemps after the flop unless he is really stupid(remember ,you raises preflop,there is A on the flop ,and you call his bet,he must be thinking what you could have and then still decides to bet).
also when you call his bets cold he will be getting the odds to draw to even inside str and even wait there with a PP lower than urs that may surface on the turn or river.
i undestand you wanna double up here but if u had 5K before the hand and doubling up would give you 10K.
after the flop you have about 3K left and you take the pot down there you will have 7K or after the turn near 8K.
with blinds of 300/600 the difference is only 2 rounds.
do you think getting them extra chips for thoes two rounds is worth risking going broke if you have the option of staying in with 7K or 8K stack?