NL100: Strange spot with AQs

[Baja15]

Villain is Unknown but has played most of the pots since they sat down an orbit ago.
I called the flop because i didn't want to push villain off their hand, as i'm usually ahead here. Is raising the flop a better line?

The turn isn't a great card but their line makes absolutely no sense. So should hero make a hero call?

OnGame's Room No-Limit Hold'em, $1 BB (10 handed) by Hand Converter CG

saw flop|<font color="#C00000">saw showdown</font>

MP3 ($109.55)
<font color="#C00000">CO ($99.40)</font>
<font color="#C00000">Hero ($98.50)</font>
SB ($41.05)
BB ($100.00)
UTG ($111.90)
UTG+1 ($143.85)
UTG+2 ($48.50)
MP1 ($193.70)
MP2 ($99.00)

Preflop: Hero is Button with A[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/heart.gif[/img].
<font color="#666666">6 folds</font>, <font color="#CC3333">CO raises to $2</font>, <font color="#CC3333">Hero raises to $7</font>, <font color="#666666">2 folds</font>, CO calls $5.

Flop: ($15.50) Q[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">CO bets $15</font>, Hero calls $15.

Turn: ($45.50) K[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">CO bets $77.4 (All-In)</font>, Hero ?