My reasoning for checking the turn: We have lots of outs to improve to what will probably be the best hand. However, if we don't hit any of them, we're not gonna win with Queen high.

If we bet the turn, they will not both fold. Perhaps neither will fold, perhaps just the one with the worse hand. Then they'll check to us on the river.

By checking the turn, we encourage them to bet to us on the river, which means if we make our hand we can raise and they'll call. If we miss the river, we can just fold.