Until this point, the hand pretty much played itself. When the K shows up I'm immediately thinking about what I can do to get the most money out of this situation. BB can call flop with A9, A5, A2, T9, Q9, J9, a whole bunch of suited connectors and one-gappers and any set (maybe would 3bet 99). Seeing as how this board was very dry and I could have bet that flop with several hands more than the BB calling range, I feel like I can lose a lot of action here. I can keep getting action from most of the 9x hands and some of the drawing hands, especially if they picked up a BDFD, but I felt like I would be folding out so much of BBs range with a bet here that checking would allow lots of those hands to bluff the river.

So what I'm asking help for here is figuring out whether it is more profitable to value bet now and likely on the river, while taking the risk of folding out a large portion of BBs range, or if its more profitable to check and give BB an opportunity to bluff with a significant portion of his range while risking the free card that he would be allowed to see.