I'm in agreement that the turn was played scared.
I think either a 2/3rds size bet should have been made, or a check (possibly a check raise, depends how the action falls).
The problem with the weak lead is that you're against 2 players, and you have no read. With two callers behind you after that flop. I'm probably not going to bet the turn.
However, if i DO bet it, i'm going to represent a strong ace, Maybe get them thinking AQ (or since they dont know you AJ), but the point is, i want them to feel that ace. Perhaps the over the top raiser was making an isolation play. If that's the case, more pressure would have stifled this.
Betting 1/2 pot, in my opinion, shows him that he can take this pot away from you and play it heads up with the all-in (and thus have no fear of being re-raised. In that case i could easily see K

x)