If he's calling down a T or a 3, (such as JT or A3) which may include a draw you need to fire a third barrel. For instance A
3
is certainly in his range, and has you beat. Would he turn this hand into a bluff? Maybe.
You check this river to induce a bluff and then you must call. Otherwise, you need to fire the third barrel.
You are never getting a K or two pair/set to fold. But you should be getting a T or 3 to fold, along with hiding your holding so people don't get the information that you bluffed two streets.
Hiding your holding is one of the reasons you fire the final barrel, and I think that reason is often overlooked. On the other hand if you fire that final barrel and DO get called, I'd almost always confidently table my hand face up immediately.
You'd be surprised at how many times people accidentally fold the better hand.