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OP's question was whether and how often to check the flop in position instead of making a continuation bet. If villain had seen hero cont. bet 100% after his preflop raises, then hero cost himself 150 chips in this hand by doing that. If on the other hand hero had checked a few draws and maybe a couple ragged flops previously, villain might have bet out here and hero saves those 150 chips.

So let's take this hand. Hero should bet most draws but check some. He's made cont. bets 100% previouly. So now, although certainly he may be giving up a chance to take the pot on the flop, why not check one? It may foil a checkraise, it may enable him to win chips against an overpair if the diamond comes, but most importantly it (1) subjects him to fewer checkraises from here on out, and (2) enables him to get chips on the turn sometimes with TP when opponent would have folded the flop, because hero's checks don't just mean made hands now, they mean missed flops too.

Cybr mentions this, check the flop only when you're able to extract value on the turn and the board's ragged, but this won't work if the table never sees hero check a missed flop after raising pf.

You also have to do this sometimes to set up some turn action that will give you a free showdown when you need it. Check-bet-raise-call on the flop cedes control of the hand to the out-of-position villain. Check-check, then bet-raise-call, lets you check the river behind, so now you're paying one street instead of three to see SD--this is invaluable sometimes but is never available to you if you auto-CB the flop, or check the flop in a predictable pattern.