I make it 11$ preflop and c-bet the flop.

As played on flop I might check raise turn/lead river if he checks behind turn. Flop action suggests an overpair just as much as the dreaded monster imho.

As played on turn I think I like a river check fold better than a block bet.

And I generally think it's okay to go broke against flopped boats when the flop is all low cards.