I don't understand your play here.
Maybe it is because I only play tournament Texas Holdem, never cash games, but I do not understand your play at all, it is a penny game and that means the players usually are pretty loose, so with a set on the flop, I would have been betting to take out the other player, he may have been holding an Ace and you need to make it expensive to him to chase, I think you slow played the flop and in loose games this can be a disaster, getting out drawn, I mean, the other player may have had the last king, with a 2 4 or 5, pocket 2s or 4s, or else A 3 to beat you, but based on the play I think this unlikely, would he call a 4X raise preflop with pocket 2s, 4s or K rag? Not likely, the big raise on the turn says full house, maybe, or straight from the A 3, my guess is he had A 3 suited, and you made the right choice to fold on the river, but the wrong play in checking the flop. That's how I learned, lol, calling on the river in a situation like this and seeing the straight come out.