My first reaction is to check the turn and call on the river... inducing bluffs from hands that you beat... as played I don't think anything that you beat is calling a shove on the turn. Everyone seems to disagree with this line though, so take it for what its worth.
What if the river completes the straight and he leads out? Surely we can't call and we won't know if we've been outplayed. What if the river is an A, and we let him get there for free with A7? The K on the turn is a good card for us because it doesn't seem to fit with any of his likely holdings.
Some players are bad. They may call you down with A7 or the naked OESD or even a pair and an OESD here. You will get called by hands that you're beating and you'll charge the ones that are drawing to beat you the biggest price that you can as well as taking away any river decisions since pretty much the only good card we can see on the river is a J. Any other card will complete another straight draw, adding 2 pair possibilities or put another overcard to our pair out there.
He's checking so I'd feel better that we're ahead now. I think this is a situation where you gotta suck it up and push it in. (not a sexual reference believe it or not)