As I begin to dig into 200NL I have come across players that will 3-bet with more than the covetted AA-KK hands. I would just like to hear on the proper methods on dealing with this and how to play back etc. Please pick apart my current strategy or high five me for it or whatever.

Against someone who your basic player and doesn't sway to extremes:

In position 3-bet with TT+, AQo+
In the blinds I 3-bet with the same hands, sometimes a slightly greater range against button players that get a little carried away.

I call 3-bets against me with:

In position (vs blind) TT+, KQs, AQs, AKs
Out of position TT+, AQs, AKs

And here's a hand that came up one time:
I bet AKs, get repopped and I call.
Flop comes all garbage, I check, he checks.
Blank turn, I check, he checks.
River is a K, I check, he pots it, I push, he called and we split with our AK
Question is should I have made a move at a different point in this hand? Should I only pull a flop c/r with a flush draw? Is the river c/r a good idea or was that risking too much or will the villian fold the same hand often enough to make this worthwhile?