You said in your OP that he always bets if you check. If that is really the case, then check-raise is good. If he does not always bet, then checking is bad because you give him a free card to draw to a flush better than yours. In this case bet/shove is better (although it will depend on his range in this sitation: do the math!)
Make an effort and do the math for a couple of scenarios (c/shove and b/shove), the same way I did above. For example I didn't have AKo in his range and I assumed he called your shove with all his overpairs, but now you think he only calls with overpairs that have a club. So he folds more (good), but your equity against his calling range decreases (bad). Also Do the math for this scenario. This will help you get a feel for the situation and you can apply what you learn to similar situations later.
One think to keep in mind is that an OESFD is an extremely strong hand if you hold two of the cards that make up the draw (like 7s8s on a 5s6sXd board). It has more all-in equity than an overpair! It is much less strong (but still often very good) if you only hold one of the 4 cards, like in your hand above.
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