Confusing hand 200NL

History: Villian is relentlessly aggressive, picking up probably 10 of the last 20 pots through betting nearly every time he is checked to and raising half of the bets thrown at him. None of his recent reraises have been called, but i don't suspect a card rush. I haven't been dealt much to combat him other than gapped offsuit cards, though i suppose i could've picked a better spot to make a stand than in the SB.

Hold'em No Limit ($1.00/$2.00)
Seat 1: ($142.00 in chips) (BB)
Seat 2: ($92.10 in chips)
Seat 3: ($200 in chips)
Seat 4: ($147 in chips)
Seat 5: ($198.45 in chips)
Seat 6: ($253.50 in chips)
Villian ($402.20 in chips)
Seat 8: ($249.15 in chips)
Hero ($318.80 in chips) (SB)

*** HOLE CARDS ***
Dealt to Hero [Tc Ac]
5 folds
Villian: raises $6 to $8
1 folds
Hero: raises $18 to $24
1 fold
Villian: calls $18
*** FLOP *** [8s 5d 4h]
Hero: bets $38
Villian: calls $38
*** TURN *** [8s 5d 4h] [Ad]
Hero: checks (maybe a mistake, though i suspect a flopped set trapping)
Villian: checks (not anymore!)
*** RIVER *** [8s 5d 4h Ad] [3d]
Hero: ? (???)

Extraction Time?
1). If so how much?
2). If not why and how do i play river?
3). What range of bets can i call?

I dont think you can bet for value here most of the time. I'd say 90% of the time I'm check/calling a medium sized bet on the river and the rest of the time value betting $40ish.

betting nearly every time he is checked to and raising half of the bets thrown at him

= check

smells a lot like 66/77 to me. I think it's better to try to induce a bluff by checking.

something is Fishy about his play... be cautious, he is smooth calling which after reading ur post is unlike villain, u said he was re-raising every bet thrown at him and betting when checked to. I smell huge hand or total shit!!!

i figured i would post the results of the hand, just so people could see what he had and comment on the likelihood of his holdings.

River:

Hero: Bets $45
Villian: (Waits for about 20 seconds) calls $45
Villian: turns over K-K (which i guess justifies his flat calling IP preflop)

I win!
But, after reading your comments and not being in the heat of the moment, i think that this hand was kind of a fluke. most of the time he probably has a set, or a drawing hand and i should check to him on the river and let him either make me pay him when he has a monster or him pay me with a missed draw (assuming someone so aggressive would try to steal the pot after 2 checks to him when he has nothing).