Thoughts throughout the hand:
Flop - I think he'll check back some AQ, KQ, QQ and AA. There aren't many bad turns, so can let me bluff on later streets with weaker value or bluffs. Also be checking back JJ at a high frequency.

Turn - he bets half pot, which I don't think is the right sizing for a draw like JTs, i think he'd bet slightly bigger, more 2/3 pot. Don't think JJ will bet this sizing either.
For value, QQ should bet quite a bit smaller to try get some back door flushes to chase. And AQ, KQ probs around 1/3 to extract value from weaker QX, T9s.

River - I think over-betting caps his range massively. With calling the turn I have all 99's, some middling pairs, TT, JJ and then QXs combos also. But i can't see any value bets he has this big other than QQ, which even then such a big bet will scare out most hands so not going to be a profitable overbet?

My thought process could be completely wrong here, but I think the large proportion of his range will therefore be be bluffs?