$1/$3 Live — Fold, Call, or Raise on Turn?

Really depends on your read on HJ.

In there 1/3 live games I play, unless HJ is a nit, I probably 3! to $40 pre.

As played the flop call is fine, but his turn bet is strong (a lot of 88+ in his range)

I'd have a hard time folding here but what river card would I like if he still keeps betting.

Your goal should always be to make your opponent's decisions hard, but by not being more aggressive preflop, you've made yours hard.

As played, I guess I call the turn and hope the river gets checked down, but I'm not happy with that.

I don't think the 3-bet preflop, at this stack dept, is a good play: he already open 4x, you make let's say 36/40 and he 4-bet to 100. You should now fold a good hand, while i would prefer to 3-bet AJ off, so all-in/fold it's and easy decision.
Even if the turn big bet( 50 into 52) screams value, i think it's a call, hoping to check it down. It's obvious you should fold many rivers. You could raise the flop but doing it here achieve nothing: worst hands fold, better hands calls or raise. It's not a range review buy i hope it was helpful.

call turn

pre could go either way. if you 3b i think you are committed with top pair on most runouts. AJ is also the type of hand that tends to fold out worse hands and get 4b or called by better when you 3b.