Thank you for responding.
1 Check call: we want to check call to allow villains to have a wider range of hands that are ahead of us and hands that are behind us when we have top pair and bet. Normally when we bet out on that flop a good player will fold weak hands and we get no value. Good players will continue with strong hands and we will be building a pot for them not us. Good villains may call that first bet but fold to any further bets. Always remember the river bets are the largest in size, it is those bets we want called not smaller polarized flop bets.
2 Check fold. This is where we need to think about being good at playing all streets by having board reading skills and strong "villain range reading" fundamentals.
On each street we get more data from the board and our villain's actions.
Your flop A96 If you check and call a flop bet will a good villain bet 3 streets vs you with KK QQ JJ 1010. Not likely. So if you are facing the 3rd bet on the river for stacks. You then think about the villain. Is this villain crazy. If yes we have to call not fold the river. Is this villain tight? Do tight villains turn QQ into a bluff on the river? ETC ETC with all villain types.
Firstly leading is not stupid. We always take actions that are correct for our villains. In this case leading was a great idea as your villain played poorly and had your villain not sucked out, you got lots of value from a weak player chasing outs.
If most of your player pool plays like this then you should be leading out. If most do not you should use the check call strategy as it captures more value.
If I knew this villain would chase I would lead out just the same way you did. In fact next time you are in a hand with this villain you should just bet bet bet with your best hands.
I hope you took a note on this villain and are always looking to be on this villains table.
As played with this villain and other weak chasers the key piece of data is, would villains bluff that river? If not then it is a check fold.
You ask how did villain know it was a good idea to call your bets? It was not a good idea. Villain was gambling.
Villain has 21% equity on that flop a call is terrible. A good learning exercise for you would be to input this hand into the cardschat odds calculator on flop and turn and look at villain odds for each of your bets and compare to villain equity on each street.
As a summary your game will improve if you work on your villain reads and board reads and how your villain's actions should relate to that data. Know how likely any of your villains will bluff rivers when pots are big.
Hope this helps.