3ball flops top two OOP, turn and river play

I was only like 25 hands in with villain, but he's running like 22/18 and his ATS was at like 4/7 or something, so he's most likely a tagg reg. this is the first time i've seen him be 3b and i don't really have much on how he reacts to cbets (especially in 3b pots). i'd been pretty active 3b'ing in ATS spots (feels good to be back at SH), but i don't know how much of that he's seen. i don't know if he's ever heard of a float

PokerStars No-Limit Hold'em, $0.25 BB (5 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Button ($47.55)
SB ($20.20)
Hero (BB) ($27.55)
UTG ($25)
MP ($30.90)

Preflop: Hero is BB with ,
2 folds, Button bets $1, 1 fold, Hero raises to $3, Button calls $2

Flop: ($6.10) , , (2 players)
Hero bets $2.75, Button calls $2.75

Turn: ($11.60) (2 players)
Hero's turn to act...

so i know that flop bet sizing is standard since he has like no draws in his range, but i really wanted to be bigger to protect my hand against over pairs. i know this throws off balance in my bet sizing in 3b pots and since this guy's directly to my right and i plan on 3b'ing him a lot, i pus out and bet standard. is it fine to bet more like 4 here?

turn is biggest question, though. i know i'm still a good bit ahead of his range, but this is a scare card to like everything i'm trying to get value out of, except for aces that floated the flop.

i REALLY don't think i can afford to check here. is it ok to b/f something really gay like 4 dollars, knowing that he doesn't have like any draws in his range?

i don't know how often he floats this flop, but i certainly think that things like AcJc and AcKc. should i just bet bet bet? a bet of like 6 makes for a pretty small river shove, but i feel like if i'm gonna bet that much, i might as well bet closer to 9

your sizing sucks dawg
you're basically telling him "here, call with a suited connector/pp pre you're IP and you have the odds"
then on the flop he peels with over + gutshot

I'd b/f $7 on the turn

PF should be ~$3.50 and flop should be like 55-65% of pot on this board, he has a lot of hands that'll yank off a card, so I'm not a fan of betting small here.