Answer: I tend to heavily emphasize checking back hands that keep my opponents dominated hands in. For example, I probably won't bet with AQ on a Ts 4c 2d board if my opponent is going to check-fold AJ or QJ, because I can dominate those hands on the turn. When he has a hand like AJ or QJ, rather than having 6 ours (like 2 overcards usually have) he instead only has 3 outs, and additionally he'll have 2 "tained outs" where he improves to top pair but I have him outkicked.
I'd almost always bet with hands which have little showdown value and retain their equity well. So, it's rare for me to check back a gutshot or something, as those hands usually make the perfect bluffs.
Lastly, I want to bet with hands that are vulnerable to being outdrawn by hands in the opponent's check-folding range. So if I have 88 on a 9c 7c 4h board, even though I can't bet all three streets for value, I'm unlikely to check because then I give free cards to hands like QJ or AJ. So on a 9c 7c 4h board, I may want to check back AcQd, since this way if my opponent has something like KcQh he can turn a dominated pair or once in a while runner runner the 2nd nut flush vs my nut flush. But I'd bet 88 because I want his KQ to go away.
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