Bet the pot on the flop and the hand is much easier to play. If you had bet the pot, most opponents with stronger holdings than top & bottom pair, would make a more sizeable raise in order to get all the money in asap. In the instance where he basically min-raised your $16 bet, he could have any combination of made hands or draws at this point and you've put a decent amount of money in the pot and don't know where you stand. You've forced yourself to put more money in and see the turn.
You show strength and bet $26 on the flop, the standard 2-4 player gets excited and makes it $75, you discount the 2 hands you could possibly beat (because who min-raises utg with Aces or Kings?) and make a difficult laydown.
If I bet the pot and he reraises me he could still have AQ (with A spades) couldn't he?
He could have AsQ, but you've narrowed his range down considerably from the range of his $40 min-raise, which could have been anything. His new range would have been - AsQ, QJ, KsQ, possibly AsJ (discounting AA-JJ because of the min-raise pre-flop and AsXs would probably smooth call).
"Now it costs me much more to find out."
Now, atleast it gives you the opportunity to fold.
If you don't want to fold, it would improve the flow of the whole hand. Betting the pot, 3-betting all-in is a much more credible line for a small flush or a hand that has him beat. It removes the horrible situation of being out of position on the turn, with $270 left in a $200+ pot.