I think turn has to be raised period. Betting gives you insight into what his range is and at the very least charges him to draw with one of the draws on board or some random crap. If V calls the turn bet you can look for a cheap showdown(i.e. a 1.75 bet into a $5 pot).

as it is I think V calls a flop bet assuming you cbet with air and has an underpair(6x or 4x, pp) or overs, or a draw, very wide range. Hero's turn check induced a semi bluff value bet on the river.

as it is call river