As for a busted draw there aren't a ton of draws on the flop. Of course any ace has a gutshot straight draw and if he paired his low kicker that might make some sense. No flush draw and the other logical draw 67 made the straight on the river. He could have the overpair, that's good. And he could have something like trip 4s (a4) or a set (22,55,88) or straight (a3).

After he called a 4/5 pot bet on the flop and a 3/5 pot bet on the turn, I would be a little more cautious on that board on the river. But that's my style. I might bet 1/4-1/3 pot on the river. There's no obvious top pair for your opponent to call along with.

As played I would be calling the min raise on the river even though it is likely your beat. At that point your getting 1 to 4 pot odds. And maybe he's got QQ or something. You only have to win 1 in 5 times for you to come out equal at the point you make that decision.

This is also my style: I like to keep my bets about 1/2 pot when I only have one pair. This is enought to protect your hand from primary draws and not give up too much pot equity. That way you don't build up a pot and lose your entire stack with only one pair. Even when you have kings and they are higher than any card on the board its still only one pair. (well technically 2 pair on this board but you know what I mean) Plus you get some weaker hands to call along when you bet 1/2 pot. Also you can make bluffs or bet mediocre hands at 1 pot to get more hands to fold, and bet your monsters at 1 pot bets to build the pot.