No hands or reads on villain.
Bet or check the turn? If we bet, what do we do if he check raises?

Poker Stars, $0.05/$0.10 Zoom Pot Limit Omaha Cash, 6 Players

Hero (BTN): $25.55 (255.5 bb)
SB: $12.22 (122.2 bb)
BB: $17.34 (173.4 bb)
UTG: $9.90 (99 bb)
MP: $7.33 (73.3 bb)
CO: $16.20 (162 bb)

Preflop: Hero is BTN with 6 A Q J
3 folds, Hero raises to $0.25, SB raises to $0.85, BB folds, Hero calls $0.60

Flop: ($1.80) T A A (2 players)
SB bets $1.28, Hero calls $1.28

Turn: ($4.36) 7 (2 players)
SB checks, Hero ?

i think bet/fold is the best approach. and i bet small in these situations (lockdown boards), around half pot or less.

Don't think you gain much by checking back here as villain is going to try and get to showdown often here when checking the turn and we can't expect villain to bet many rivers. My default is to just bet here when checked to in both the case that we have a value hand and when we peel this flop with some marginal KQJx, JJxx+ etc. Sizing should be consistent and doesn't have to be too big.

Villain 3-bet out of the SB, so without reads it's likely a strong range, with KK+, lots of broadways, or a decent rundown with at least one suit.

Flop hits his range harder than your range, so his c-bet looks pretty standard. When you call the flop, I think your perceived range narrows significantly to a T or better, possibly with a gutter to go with it.

When villain checks the turn, he's either giving up with a hand that missed (if you call the flop, you're unlikely to be folding on this turn card), hoping for a check through with a straight draw or turned flush draw (and hoping to get it to showdown if it hits), or going for a check/raise with AT, TT. I don't know what part of his range would check/call. I would be surprised if he check/raised the turn on a paired board with any straight or turned flush draw.

So I'm bet/folding the turn, probably just over half pot.