my image is of a competent, villain is a thinking LAG, can be aggresive and bluff with air.

1/2 NL - 7 handed home game

SB villain (700)
Hero BB (550)

UTG limps, BTN limps, villain calls, hero with J 7 checks.

flop (4): K 7 2
evrybody checks. table was very aggresive so i decide to check my second pair.

turn (4): J
villain bet 4, i raise to 18, UTG and BTN folds, villain call. i put villain on a flush draw or a weak k or J.

river (44): 8
villain checks, i bet 25 trying to get value from a K, villain raise me to 80. this was a realy strange raise in my mind. it make more sense to me he's bluffing with busted flush draw, then anything else

should i call this? should i have checked the river?

Easy call in my opinon. Playing a LAG this deep I just can´t find a fold. He could have missed a draw or have 78 or just biting on the fact that you checked the flop.
No checking the river plz.

Bet/call. Small chance he has 9-10 here but it looks like he rivered J8.

In all seriousness, is the Jh in your hand or on the board? If it's on the board, that opens up a wider range of hands Villain can bet/call turn and check/raise river with if he's really a thinking LAG. Without knowing this, Villain is likely value-towning you.

This happens to be a leak in my game, but I always call here, even though I beat only a small range vs. a thinking LAG who pretty much knows your range here. Villain sees you're trying to build a pot on the turn, probably knows you're betting the river (his check and not a blocking bet of his own on the river tells me even more that he's got you beat), and just got at least another $25 from you with the opportunity to make another $55. This river bet basically tells you he had you beat the entire time or got there with the big draw (9h10h). I'm guessing Villain NEVER turns over a top pair type or 7/8 here.

With all that said, bet/fold the river vs. this specific opponent. There are plenty of other opponents against whom you can bet/call and be good, but if this guy is really a thinking LAG, he's likely got you beat.

I don't think either bet/fold or bet/call is horrible. Given that villain can bluff with air I'm inclined to call this.

I don't think he c/r the busted flush draw unless he knows you well enough to trap you that way. He would bet out.

Neither would Kx c/r unless he has the higher 2P.

All other hands would fold if behind and raise if you are beat. fold.

There are a lot of situations where I would check that river. If KQ and KJ would have raised flop (maybe K10), then only K9/K6/K5/K4/K3/78 calls you and loses.

bet the river always here, now fold. (unless villain thinks that you are very aggro semi bluff raising etc very often), if so, then call. But if all is standard with images etc, this is a fold. The raise size can only work as a bluff if hero has about total air, so villain must be pretty confident that air is all we have to make this size CR.