flopped set still lost

flopped a set of 7s, mid position, three-way to the flop. two checks to me, i bet about 3/4 pot, one guy calls. turn’s an overcard king, check to me, i go about half pot, he snap calls again. river bricks, i go for value small, and he jams over me. felt wrong but i made a crying call, he flips over pocket kings for the higher set.

just can’t decide if i played this wrong or if it’s just a cooler you gotta eat sometimes. in my head, i know sets are tough to fold, but now i’m thinking through every street, wondering if i should’ve checked back turn or somehow found a fold river. maybe i just overvalue my hand against these super passive lines. anyone else replay these spots in their head for hours?