Raise preflop. You are button, which means that if you get called you are in position (good to get the more value out of your set if get it). It also may offer you some free blinds. I think a call is not too wrong, but it is so weak...
Your overbet on the flop (to build the pot I guess) might be effective because you don't have much fold equity on NL2. However I would only bet pot max. If you want to play a big pot just raise preflop (that's another reason: playing big pots with your set!)
turn: fine for me.
As for the river, it may seem tough. You are behind 66 or TT. Straight is also dangerous. He might also have something like T7 or T8 to play like that. Given his AF it seems dangerous to play your set here. I think I would have fold too, but really wondering if my play would not have been too weak. I'm interested in the evaluation you will get for this hand