Hero only has TPTK (maybe) and needs to know where he stands ASAP. I think the pot bet at the flop is good play because it forces the Villain to play -EV on a draw, or getting valuable information about a stronger hand.

On the turn I am checking. Either he is playing -EV and you won't be able to shake him, or he has a made hand. It allows you to see what move he makes, and that will be invaluable in playing the River. It also lets you get there cheaply, or you can just get out of the hand altogether.

Getting into a pot for 2/3 stack with TPTK is what you want other players to do with your made hands, not the other way around.