if it is true that the BB has a propensity to bet with nothing , then I like raising the turn with our flushdraw+two overcards better than calling. Given that the CO's hand is still not defined, and the CO views the hero as weak tight, we may induce the CO to lay down a better hand(The CO will fold AK too and that is also wonderful) The hero has to call the turn anyways, so investing one more BB to possibly increase the hero's chance of winning this decent sized pot is worth it in my opinion.