I think you shouldn´t play check/call with a top pair top kicker in that kind of board.
In the flop you get TP/TK and the bet is correct.
In the turn, i don´t think the 3 in the make different the situation. You are the preflop aggressor and he called. Here, a card like the 3 probably is not in his range and you should have the best hand. Maybe his range be broadways, Ax, some high and medium PP and some suited connectors. Also, the board shows a flush draw and a straight draw, maybe if he has a draw, he would like a free card, probably he would not bet (but he did it). And finally, if he would have 33 (is not very probable, but let's assume it) with his set wouldn't bet as strong as he did it because he would like to extract more value of his monster.
Then, the Check/call in the turn isn't correct. The best line is a second barrel.
And finally in the river, is completed the straigh and again you check. Here you think probably he has something like the straight or two pairs or something better than your pair. But żDo you think he would have bet that size having the nuts? I don't think so. he would like to see your call and wouldn't go allin. the other hand is that he would have two pairs and the straight scares him, but one can't win all the hands.
Sorry for my english, i'm beginer