.50/$1 home game

V1: ($180): don't know this player very well except from a tourney environment, where he has made the final table several times. Seems to understand outs/equity, and play a non-ridiculous amount of hands. Rarely limps.

V2 ($80): plays often, but has no clue overall. PFR somewhere around 40%. Perpetually amazed when he loses pots due to bad kickers.

V3: ($60): not important to this hand except that he calls preflop and adds to the pot size.

Hero covers all.

Towards the end of the night and we're playing 5 handed. I open AT UTG to $3. V3 calls OTB, V2 calls from SB, V1 calls from the BB.

Flop ($12) KJ2.

V2 bets 2.50 (lol). V1 raises to $5.

This raise was really interesting to me, because my assumption would have been that this TAG would know better than to just auto-double a bet to raise it, the way most inexperienced players do. The other reason it's interesting is because I feel like there are very few hands he would make this raise with (I will leave out my assumption of his range in order for others to make their own analysis).

I am 100% sure V2 will call the raise for 2.50 more, So right now I have to call 5 to win 22, perhaps 27 if V3 comes along also. I call. V3 folds. V2 calls.

Turn: (Pot $27) Q.
V2 checks. V1 bets $15. I raise to $35. V2 folds. V1 takes a good 30sec to think and then calls.

River: (Pot $97). 4. V1 checks. Hero ???

I have spent most of the afternoon contemplating both villain's range, and his assessment of my range, trying to formulate the perfect bet size.

First off, you villains are confused here.
And it makes a bit a difference. (You say V1 folded in on the turn, but he checks the river?...)

Is V2 or V1 in the por?
If it's V2, this is an auto ship every time. He has so little left we can't do anything else as he's put in ~40 into a the pot, has $40 left so we should shove.
But i'm assuming it's not otherwise this isn't a thread.

So, if it's V1, he cold called a bet and a raise on the turn so I would bet $50 or so here hoping he can't laydown whatever he has which is most likely two pair.

Also, I think the flop is a fold with only 4 clean outs (maybe 3 if someone has KQ or QJ). Sometimes we have 6 - 7 outs total, but even still it feels like a fold.

villains corrected. You were right, V1 is the one who stays until the river. Let me re-state with names FISH and TAG:

Flop ($12) KJ2.

Fish bets 2.50 (lol). TAG raises to $5. I call. Fish calls.

Turn: (Pot $27) Q.
Fish checks. TAG bets $15. HERO raises to $35. Fish folds. TAG takes a good 30sec to think and then calls.

River: (Pot $97). 4. TAG checks. Hero ???

Fold flop.

Raise turn bigger.

As played, $65 sounds fine.