I'd say given his passivity throughout the hand and his board, he's unlikely to have a hand which beats a pair of aces, and it's very unlikely he can beat aces up. Assuming he's a typical player, he won't raise on the river with two pair, but he will probably bet if you check, and I assume you will always call a bet if you check the river. He will also probably call the river with a pair. This means that you lose an extra bet every time he has two pair, regardless of whether you check or bet, but if you bet, you gain a bet when he doesn't. And as was said, if you're raised, it's an easy fold, so if he improves to trips, you still lose only one bet.