I don't think there's too many reasons to bet the flop with 3rd pair. Would hate to bet and get raised (would fold), it also doesn't help that we have the Qs meaning they have fewer draw combos to call with.

Turn I'd have checked back again, don't think we can get value from worse too often.

I like the flop check. No need to turn your hand into a bluff just yet.

I also like the turn bet but would make it around 10c, which I would expect any pair or spade to call. This way you get some super thin value and protect yourself against him leading out on the river as a bluff.

I wouldn't expect villain to check Ax to you twice so we're only really worried about him having Kx.

Pretty std line from you imo, dont think there's any good reasons to cbet this flop. Turn is good to bet for some thin value, can be betting slighter bigger tho.