Top of range or his only holdings?

[LondonImp]

One of those pesky hands where I'm not sure if I've run into the top of his range or this is all he has.

Doing this from memory so may be slightly off.

6 max

LJ xx bb
HJ xx bb
CO xx bb
BTN 240bb
SB 106bb
BB (Hero) 240bb [eff] - AQs

Preflop

LJ: Fold
HJ: Fold
CO: Fold
BTN: Raise to 2.2bb
SB: 3-bet to 9bb
BB: 4-bet to 22bb
BTN: Fold
SB: Call

Flop: AK3r (~45bb)

SB: Check
BB: Bets 14 bb
SB: Call

Turn: AK3 Qr (73bb)

SB: Check
BB: Check

River: AK3 Q 7r (73bb)

SB: All in for ~70bb
BB: ??

I mean there's nothing to do here other than just call right? But the only hand that really made any sense for him to do this with would be AK. Which of course he had. I need to be good >33% of the time to profit here and against an unknown villain I just don't know...

[kkep]

shitty spot but I'm paying. checking turn under rep's our hand somewhat and very much so vs bad players.