Hey Danwan, I think I'd check back turn as I feel like we only get calls from better.
Also the idea of a protection bet is to get folds from worse hands with equity, so with the price you're giving you do not achieve this.

There's a chance opponent can have hands like 66 or 77, so I'd probably check back and go to showdown as we beat them anyway.
Also vs a 9 if you check the turn, they probably check river and you save money anyway.

Flop is a spot where I check back now intending to call the turn then re-evaluate river. If we're ahead villain likely only has 6 outs, and we're not really getting any value.

As played I would definitely check behind on the turn because those 6 outs now only have about 12% equity and villain is unlikely tobluff any smaller pocket pairs as a bluff on the river.