Villain is a 24/18 reg and my image is TAG. Hope to hear some good advice on what sizing to use with our whole range, thanks.

$2/$4 No Limit Holdem
Stacks:
CO ($400) 100bb
BTN ($813) 203bb
SB Hero ($410) 103bb
BB ($396) 99bb

Pre-Flop: (6, 4 players) Hero is SB 7 A

2 folds, Hero raises to $12, BB calls $8

Flop: 10 3 2 ($24)
Hero bets $18, BB calls $18

Turn: 9 ($58.50)
Hero bets $44, BB calls $44

River: 10 ($146.50)
Hero?

I would start by thinking about villains hand range. How strong is he to call twice here? can he just have a big spade? Im actually between betting and checking here. If he has a T i think he bets it anyway, although maybe a slightly smaller size then he would call, he probably fires all his missed spade/straight draws. We probably loose value from 9x and some over pairs but idk how much of his range is that anyway after not raising pre and calling twice. If he ever has just a big spade i like a c/c, c/r is too think i think even against most Tx.
If you think betting is the right play i like a bigger bet, 2/3-3/4 pot range to get max value from Tx.
Checking also stops you from getting raised and being put in a SUPER gross spot

I think our triple-barrel range should be very polarized here and thus, i like betting really big with all hands that want to fire a third barrel.

if you would bluff with the naked As here then go ahead and bet 3/4 pot. if you would give up it with it check raise allin

I kinda like a check too because of that.

The question is, does this hand goes into our 3 barrel range?

I would give up on this river with my bluffs.

Thanks for the replies so far guys.

bet 80%pot+

don't think you should have one betsize with your entire range

1. I think any 10x hand is likely.

2. as played on the river I would check call.

3. alternatively, he probably polarises his range quite a bit with possibly K of spades with a 10 so maybe a 1/3 bet is nice too. probably folding a shove on that river.

what did he end up having?