Hard for a passive player (based on pre action) to have a worse value hand to bet two streets here. The three diamonds should scare him aswell. It is BTN v BB tho, so in some cases this may be a thin call. Against some random scrub fish I can't see him value betting worse a lot, and bluffing as seldom, so I think it's a fold most of the time. The thing is that he will prob check back QJo on the river, scurred of the flush.
Edit: btw betting turn is fine, and would change the entire dynamic in the hand. Kind of read dependent when u go freestyle with the check on the turn
Bet less on the flop imo, around 4.5/5bb.
Turn isn't great for us but I wouldn't fold here, calling is fine, villain might lead out with worse Qx hands here, possibly J10 109 etc with a diamond and just the A/K of diamonds.
On the river i'd be worried, this bet basically wipes out the hands i've previously said in his range, he's repping a made flush, an 8 or a straight, more likely a flush imo. Folding is best option here.
On the turn you really want to keep control of the pot , so check calling is the best option IMO. villians range 8x j10s,J9s , qx possible flush/straight draws which may have completed. Betting here will just get you into a tricky spot.