Villain is a TAGgy regular. 24/17/2.1 (VPIP/PFR/AF) over ~270 hands.
$2 NL (6 max) - Holdem - 6 players
SB: $161
BB: $218
UTG: $63
MP: $157
Hero (CO): $290
BTN: $245
Pre Flop: Hero on CO has 7⋄ 6⋄
2 folds, Hero raises to $8, 2 folds, BB calls $8
Flop: ($17, 2 players) K⋄ T♣ 6♥
BB checks, Hero bets $15, BB calls $15
Turn: ($47, 2 players) K⋄ T♣ 6♥ 3♠
BB checks, Hero checks
River: ($47) K⋄ T♣ 6♥ 3♠ J♣
BB checks, Hero?
Bluffing the river after checking back turn here is not a good idea. The only hand you are representing when betting the flop, checking back the turn here is like AQ or JJ. You will get too many curious calls to be able to successfully bet the river here. If you want him to fold low pairs etc., you will need to barrel the turn and possibly the river as well.
When villain calls this flop his range consists of hands like QJ,JT,T9,KJ,KQ and alot of other low-medium pairs. I would not put him on a particularily strong range since I think an aggressive player like that will most likely 3b these hands preflop.
I would prefer you to check back the flop here to keep the pot small and try to get the cheapest showdown as possible.
You can only succesfully bluff, when you know BB will never have K and almost always have a T and you are known of value betting light with something like AJ. Actually I like the bet more, as you represent AQ, JJ, KQ, KJ, TJ maybe even AK and he almost never has KQ and KJ because he would bet the river with those hands. Also unlikely that he has a huge hand like a set (AQ probably never, as against CO range it's good to 3-bet and he is a taggy opponent so knows that) and want to check-raise it on the river. I dont agree with @Duffman1985 that villains range contains JT, and KJ, because he should probably bet that against our mid hands like Kx, and QJ, AJ, because we are most likely to check those hands rather. The only very strong hand he can have is TT and 66 and this line is not standard at all with those. He can fold a lot of T like T9s, TQs, AT, these are the most probably hands he just cold calls with preflop. Maybe you can even represent QQ too. and as there were not very much draw at the flop, not even the turn ! it's more likely that you have a value hand that became real value hand at the river. So I dont think it's very profitable him to call with Tx and even with Jx. When you have a good table image, this even goes toward the bluff I think.
Pre
I don't agree with opening for 4 bb with 76s.
That is the type of hand that plays well multi way.
Come in for 2.5 to 3 bb.
You are making these speculative hands too expensive.
That hand does not have enough equity to be on an expensive steal here.
If you are flatting some good hands here then just flat. If you don't flat open here then fold.
Call an open here is great and also just call with some strong hands makes playing this kind of hand affordable and profitable.
In reading your hands in general I feel like you make lines too expensive. You can still get paid off when you hit.
Flop
BB called big raise pre so K and T are in their range. Pre flop aggressor, bottom pair, two runner runner draws. Yes take a stab at the pot. Why make it so expensive? What does $15 do that the $10 will not? Given you over-bet pre you can rep AK, KK, TT and get a fold with $10.
River
J is also in villains range. Cannot fire into this after checking the turn.
