Second level of a live MTT, blinds at 50/100 with starting stacks of 10,000. Effective stack c.9,500.

Action is folded around to Hero in late position with 99. Hero opens for 300 and gets one caller in the small blind (too early for any concrete reads, although he had been fairly active already).

Flop: J83 rainbow. Villain checks, Hero bets 425. Villain raises to c.1,500. At this stage, I didn't have him on an overpair given he hadn't 3-bet, nor a set, since on such a dry board the general population tendency is to check-call the flop (and possibly turn) and let the pre-flop aggressor continue to volunteer money. It's possible that he's got a J10-type hand and is betting for protection, but I called as the check-raise felt a bit bluffy and 99 is too solid a hand to give up at this stage.

Turn: 6. He leads out for c. 3,000. I tank for a bit, but ultimately fold, choosing to wait for a better spot. The lead out felt weak, but how much heat can 99 really take?

What do you make of my line / reasoning? Would it have been an idea to shove over the top on the turn, putting him to a difficult decision or is it better to walk away with over 7,000 chips left?