4/8 Live hand - How do you play the turn?

[RitaNg123]

I haven't been playing live limit as much as I used to, and I'm sure I've had a similar type thing happen before, but I thought I'd post for feedback and help. It might seem kinda straightforward, and I think I might just be posting to reinforce things in my head...

I am in LP with AQc and there are 2 limpers before me. I raised it and got one cold caller behind me, SB folded, BB called, and 2 limpers called. The flop was: A-4-8 rainbow

It was checked to me, I bet, cold-caller raises, and it's folded to me. I 3-bet it, and he caps. His cap worries me a little, and I start to wonder what sort of range I can put him on. 44 or 88 seem to make the most sense in terms of what he'd cold-call preflop for 8 at a typical 4/8 game (well, I guess almost anything can be cold called in a typical 4/8 game) and I considered A4/A8 as possibilities. I didn't think he'd cap something like AT-AK, although I really didn't know at this point.

The turn is a Q.

What do you do?