When you check-call the turn, you pretty much commit yourself to calling his slightly less than half-pot shove on the river. If you were behind on the turn, while 5:1 pot odds may look nice, how many hands can he reasonably hold where it's mathematically correct to call with your two-outer?
And if you're ahead on the turn, then you're still ahead unless he had 88 or 67. The probability of that seems too low to fold getting more than 3:1 after he shoves.