Villain is running 49/0 after ~90 hands. His aggro per street is pretty low, but it spikes to 13 (!) on the river. The only decent sized pot you've seen him show down is where he lead 3 streets with the 3rd nut flush draw which hit on the river (40bb pot vs someone else). He was betting small the whole way and potted the river.

Hero has been pretty in line and somewhat active. I was running like 25/22 because I kept getting decent hands. Won a lot of pots without showdown, and made a few big raises on the turn/river which never got shown. The only big hand I showed down was AK which I got in PF.

Poker Stars $0.05/$0.10 No Limit Hold'em - 6 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

UTG: $20.75
MP: $22.60
CO: $7.00
BTN: $7.50
SB: $9.90
Hero (BB): $19.10

Pre Flop: ($0.15) Hero is BB with 5 3
UTG calls $0.10, 4 folds, Hero checks

I'm not raising this PF.

Flop: ($0.25) K 7 9 (2 players)
Hero checks, UTG checks

I'm not betting this type of flop vs his limping range.

Turn: ($0.25) A (2 players)
Hero bets $0.15, UTG calls $0.15

Well, now I can bet. Picked up a flush draw and our stacks are so big that I feel that if I lead here and get raised it's ok to call because if the A helps him he'll probably put in a lot of money on the river if I catch my flush.

River: ($0.55) 4 (2 players)
Hero bets $0.55, UTG raises to $1.70, Hero raises to $4, UTG raises to $6.30, Hero ???

I hit gin but I have the worst possible flush. After he popped it to $1.70 I narrowed his range to:

bigger flush, 77/99, 2 pair, Kx, Ax, weak 1 pair hands, wiffed flush, wiffed broadways

I figured enough of those hands (which I beat) would call a raise so I made it $4. I think a lot of 2 pair, Ax, maybe even KQ would call (maybe he doesn't put me on an A because I didn't raise PF).

Then to my surprise he re-raises. He does have a high river AF but still, we're in a limped pot and I bet the turn+river+raised his raised and now he's re-raising me again. Surely he must have something he really likes.

I think the only move here is to call or shove. If we shove, it's for an additional +/- 1.4 buyins which is pretty substantial. Which line are you taking?

Edit:
Also, what do you do if he just shoves after you re-raise to $4?

call, his line looks like a flush a lot and you have the nut low one, i dont think he ever 4 bets this river without a horribly played set or spazzes out with 2 pair.

call with small flush here - obv if it was a T or J flush id shove

dont get the money in , 200BBs unraised, if you dont have the nuts.

3betting the river is obv. spewy because you have the worst flush possible.

Im only 3betting w/ QdXd.

Notice his final reraise there is a minraise. Fish that do this almost always have a big hand. You can't fold, but raising would be a big mistake imo. Just call this.

I don't know...

If it were clubs on the river and we had 35c then it might be spew to raise here but it's a backdoor flush and this villain is super ultra mega aggro on the river plus seems to over value his hands a bit too much (going by stats/what he's shown down in the past).