Let's talk Vader.

Vader didn't even know about Leia until Luke leaks it in RotJ. During the Vader/Luke duel is the first and only time Vader acknowledged Leia. Luke's thoughts turned to her during that fight. Vader saw that "weakness", the attachment, and he leapt on it. And it worked (for a moment).

Now it's possible Vader had a rough idea of her existence near the finale of Empire. Luke calls out to Leia. Leia is with Luke when Vader calls out to Luke. I expect Vader was too distracted to notice Leia.

Back to A New Hope. Vader doesn't suspect anything until Obi-wan shows up on the Death Star. Why is Obi-wan here? What is he doing? Then he just disappears? Something about the crew he arrived with is suspicious. Then during the Death Star trench run. He is focused. Vader can sense something. Vader can sense something that can not be. Obi-wan has a Padawan? Why now? Who? Then Han Solo fires at him. Vader should have seen it coming, but he was distracted.

Sooo! Vader seeing Leia opening? He just had no idea.