I like a bet on the turn. Most hands he has have decent equity against you so you don't want to give them a free card, especially since by playing your hand that way, you will be forced to pay him off on the river when he may be bluffing with a frequency that makes it tough for you to make money.
Also if you check and a spade comes off on the river, not only have you missed out on a turn bet from hands like ATo, now you may actually get bluffed off your best hand on the river.
The ranges I put in flopzilla show him having top pair about 40% of the time after he calls the flop and a flush draw about 20%. When he doesn't bet the turn, it's less likely he had a flush draw. Charge those weird single spade hands, get paid off by those weaker aces, and keep yourself from getting bluffed on the river. Bet the turn.
As played, any reasonable range has you at 35% equity or better. Call.
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