[rikz]

The stop & go min-raise from villain looks like a strong hand more than a bluff or a weak ace (AT?). So, he must think he's ahead on the flop and the turn. What hands would he call your raise with from the BB that are strong on flop and turn to play this way? Well, he might have AQs (TPTK turns into 2-pair on turn), T9s for a straight (but this is a loose call oop, so less likely), and 88/JJ (set on the flop). Less likely candidates include a KT for a straight, but that seems unlikely for him to call your raise with OOP from BB, and I think a villain with QQ might have reraised preflop.

So, where are you on the turn if villain isn't bluffing with air or an unimproved low pair or a low flush draw (or whatever):

Holdem Hi: 44 enumerated boards containing Qs Js 8c Ad
cards win %win lose %lose tie %tie EV
As Ks 15 34.09 29 65.91 0 0.00 0.341
Ac Qc 29 65.91 15 34.09 0 0.00 0.659

Holdem Hi: 44 enumerated boards containing Qs Js 8c Ad
cards win %win lose %lose tie %tie EV
As Ks 11 25.00 33 75.00 0 0.00 0.250
Tc 9c 33 75.00 11 25.00 0 0.00 0.750

Holdem Hi: 44 enumerated boards containing Qs Js 8c Ad
cards win %win lose %lose tie %tie EV
As Ks 11 25.00 33 75.00 0 0.00 0.250
8d 8h 33 75.00 11 25.00 0 0.00 0.750

Without doing all the math, I think you are a little better off than 3:1 behind and you get better than 4:1 to call. So, I'd say call the min-raise on the turn, check behind on the river if villain checks, and consider folding if villain pushes that 5d river card.