[spydog]

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Because if I bet the turn I am for sure beat if he raises again, and I can fold. If I check and call the turn I will feel compelled to check and call the river too if it blanks out. Didn't stick to my plan though.

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I think I became a better player in HU situations when I started to look for reasons to showdown and quit looking for reasons to fold.

Also, in the hand that you posted, if you have a passive read on that player then you need to check-fold the turn unimproved because passive players do not 3-bet flops without an overpair. If you think they can then you need to commit yourself to showdown as cheaply as possible by check-calling the turn/river.

I can't think of any type of player, barring a very, very specific read, where I would take your line of calling the 3-bet and bet-folding the turn, regardless of the turn card.