I think I missed out on value OOP in a 3-bet pot - how should I have played it?

Playing 1/2 at the Hippodrome in London; had been quite nitty given that it was the end of the night and the 2/5 table had just broken with 3 of those guys coming over to play at our table, but I had 4-bet KQo and shown the previous hand so that probably gave me a slightly looser image.

£5 straddle is on and cutoff player (2:5 guy) opens to £15. Hero looks down at TsTh in the BB and 3bets to £50, cutoff calls.

Flop: AT9 rainbow (pot=106)

I range c-bet £50 and villain makes the call.

Turn: off suit J (206)

I check (I think in hindsight this is a mistake; I was too scared of monsters under the bed like JJ and for some reason KQ but obviously that’s a 4bet bluff or a fold on the flop in retrospect)

Villain bets 125

I call

River: 5

I check

Villain checks back

I show the set and I’m good.

I think I should have gone for a small sizing like 75 on the turn to get value from hands like AQ and AJ, which he has a lot more of than he does JJ.