Could do with some feedback on this hand if possible guys, thought process as follows:

Villain has been defending BB quite wide, on flop I decide to Cbet to fold out majority of his calling range and to protect our equity, turn I decide to bet 66% of pot to get him to try fold out his flush draw, A3o, random 98, TJ, etc and also the K hits our perceived range. now the river is interesting as he checks, all draws miss but I thought by betting here to put him in a tough spot if he holds K7, K8, K6 K5, we have shown strength.... question is do I shove river? I feel a check back is quite weak? I was disappointed to see him show K6o to say the least, could he have folded the river to a shove? not sure