NFD in 3-bet pot; do I blast this Turn or take a free card?

Note: Blinds are $1-$2, but game is $2-$100 spread-limit, which means the most you can bet is $100 over the previous amount. So if I bet $20, you can raise to $120, I can reraise to $220, etc. Max buy-in is $300.

Splashy Friday night game with lots of deep stacks. I just table-switched to join it but don’t believe anyone noticed. I have a stack of $240.

Villain has a stack of like $1500. One HH of note: he cold-called my 3-bet with 78cc from the Straddle. We all checked a JT2 flop. He led big on a 9 Turn, Opener called, I folded. River another 2, Villain bets $100, Opener max-raises to $200, Villain calls, Opener shows him KQ.

This hand: I open AsTs from the CO to $10. Folds to Villain in BB who 3-bets to $25. I call.

Flop: Qs7s2h (pot: $50, heads-up)

Villain bets $50, I decide to just call this one, as I think a raise on a board this dry is too transparent.

Turn: Qs7s2h 6d (pot: $150, heads-up)

Villain checks. I now wonder if his hand isn’t a scared pair of JJs or 99s (or a whiffed AK) that I can steal with a $100 bet, repping an AQ that wants to charge his flush draw. Or should I just check and take my free card? What do we think? I have $165 and he covers me.