When you jam the flop, what is your bluff based on? Clearly you want him to fold, but from the text in your OP, it looks like you are only considering your own cards when you jam. You need to try to consider what the BB called with pre, and then called again with on the flop, and decide how much of his range he is likely to fold to your jam on the turn.
When he called the flop c-bet, his range is pretty much made flushes or high flush draws, sets, two pair, or top pair hands.... and how much of this range do you think he will fold when you jam the turn? You note that you have a straight draw, but you could be drawing dead already.
I much prefer to check behind on the turn, and then re-evaluate on the river.... if he checks again, a river bluff might get through, particularly if he has missed his draw.