No, I agree that his range is weak when he raises the flop, but it is only weak because your c-betting range is very weak.  You are oop though, and don't want to balloon the pot with sucha marginal hand.  The reason you flat his 3-bet are the same reasons you want to check call imo.  I wouldn't look at it as just this one hand, but as what works best against his range.  Your hand is somewhat strong and has outs against most hands, but I don't understand why you would lead this flop when you are repping a super thin value range, and any competent opponent will put you in a tough spot like this with a wide range of hands.  The only way you are going to get value from the hands that you beat on this board is calling, because he is folding any pair that doesn't have a big diamond(better than yours most likely) or any non-king.  So when you bet you are only getting called by hands that beat you.  It seems like he understands that your range is weak here, but he doesn't know how to best utilize this information.  He should be floating almost his entire range here, then taking it away on the turn.  By raising, he reps a much thinner range of value, and you are correct in calling flop IMO, I am just arguing that against any competent opponent and against poor oponents, checking flop is way better.  In this case he raises, but most of the time they won't spew and raise flop but either fold or call.  When they call you are basically ****ed cause you are oop against a range that has you pretty crushed, and when you check and he bets turn here you are in a really tough spot.  In this instance betting the flop may have induced a spew, but against his whole range i think it is way worse than check calling. 

yay you won the hand! I was really wondering what he had and I settled on AdQx, but I am glad to hear you won  Also you got max value lol where I probs would have gotten less