Preflop descriptions:

Hero: Straightforward tight-aggressive player. Has only showed down big pocket pairs basically. Has an image for being extremely tight, but did show a c-bet bluff once.

Villain: Standard fish. Known as the table ATM. Not too sure, but doesn't seem to observe other player's images much. Extremely loose-passive preflop (called 35 preflop with K3), unpredictable after flop. Will chase draws with unfavorable odds, bluff & float, frequently check-raise big hands on flop, but will also bet for solid & thin value. Seems to do the above at whim rather than after careful calculation, however.

$2/5 NL home game

SB Hero
BB
UTG villain ($1100)
MP hero ($600)
MP
LP 1
LP 2
Button

Hero is dealt AK

Button straddles $10, SB folds, BB calls, UTG villain calls, Hero raises to $40, Folds to UTG villain, UTG villain calls.

Flop ($100): 977

UTG villain checks, Hero bets $65, villain calls.

Turn ($230): 4

Villain checks, hero checks.

River: 9

Villain looks at flop and then looks back at hand a couple of times, and bets out $125. Hero?

Should hero ever call here with A-high?

I think this guy would have probably donked flop/barreled turn with 7x or 9x or an overpair. He reps nothing; I'd call.

I feel like villain would bet counterfeit pocket pairs as well as other As maybe even K high if you have history. I could see a call here being profitable with implied massive tilt odds with you calling his big river bluff with A high.

yea

Based on my description, what do you put as villain's range here?

Based on your read, I would call.