You end up OOP so I'm finding both pre-flop and flop slightly uncomfortable, but the main thing I want to comment on is that you seem to think your flop bet is big and that a smaller bet could do the job.

The flop has a flush draw and a straight draw possible (including combo draws) and the K high nature of it makes representing the K with a PSB designed to price out draws perfectly plausible.

Betting 1/4 pot on this turn as a blocking bet to make sure that you're getting the right price on your draw is a great play when it works - where against many good opponents it probably doesn't. At the stakes you play it can work and when it can work there's no shame in it.

You're getting pretty decent value out of the hand - I don't see how it could have gone that much better. Maybe a slightly bigger flop bet ($0.40 making a $1.26 turn pot - $0.30 turn bet making a $1.86 river pot - $1.5-$2 river bet). Or maybe just exact PSB the river or overbetting it slightly could have worked. But it's easy to be results oriented - in the hands where you wouldn't have rivered your straight you'd have lost correspondingly higher amounts.