When the movie came out it wasn't obvious. It is clearly stated why Luke would have believed him, as Vader asks him to “search your feelings you know it to be true”. So either deep down he already realized it or it is more of a force thing.
One idea was that, upon taking off Vader's helmet, Luke would place it on his own head and state that he was Vader now. From there, he would go on to destroy the Rebel fleet with his new resources. George Lucas immediately shot the idea down, stating that the movie was supposed to be something enjoyable for kids.
It was the fact that Luke was his son that caused turmoil within Vader. It was his love for his son that caused his loyalty to Palpatine and the Dark Side to falter. If Vader didn't know who Luke was he would have been just another force sensitive person to be trained to serve Palpatine like an Inquisitor or be killed.
The Emperor commanded that Luke finish his father and join the dark side, but the young Jedi refused, opting instead to throw away his lightsaber. Enraged at this denial, the Emperor shot Force lightning into Luke, torturing him. Vader rose, the good in him awakened by his son's compassion, and destroyed the Emperor.
While villains such as Vader and Kylo have used mind probing to undermine their enemies, Luke himself strayed into the dark side when he betrayed his nephew in The Last Jedi's flashback. Mark Hamill criticized these changes to Luke's character because it defies everything Luke symbolized in the original trilogy.
New ‘Return of the Jedi’ footage CHANGES Darth Vader
Why is Vader so weak against Luke?
Since Anakin's defeat on Mustafar, he needed frequent visits to his bacta tank to survive, and even the Vader suit itself was crude enough for Palpatine to control him. So with an aged body, a mind out of balance and the surprise of Luke's attack, Vader was caught at his weakest point.
Vader's only goal in the fight was to make Luke lose control of his emotions and bring him closer to the dark side -- and that's exactly what happened.
Darth Vader may have never known Princess Leia was his daughter in Star Wars and never cultivated a relationship with her, even when he was a Force ghost. Anakin Skywalker never knew Padmé was pregnant with twins, and he believed his child had died with his wife.
While Darth Vader's obsession with Luke Skywalker in The Empire Strikes Back is seemingly due to the latter's destruction of the Death Star battle station, his revelation to Luke and brief dialogue with Emperor Palpatine recontextualizes his pursuit.
It is well worth remembering that, as far as Vader knew at the end of "Revenge of the Sith," he had killed Padme and his child did not survive. It is also very important to point out that he had no idea Padme was pregnant with twins. This will come into play as it relates to the Leia situation.
While Vader may be stronger, Luke had several advantages of his own. He was both swifter and nimbler than Vader. But the biggest edge was that Luke didn't give in to his hatred and anger.
Vader's redemption in Return of the Jedi was not just about saving his son; it was also a defiance of the dark side's corruption and his own past as a Sith Lord. Vader's decision to block Luke from killing Palpatine was motivated by his knowledge that it would corrupt Luke and lead him down a similar path of suffering.
Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection. Vader's denial of Anakin Skywalker's legacy and his fear of getting hurt again prevented him from realizing the truth about his children until later in the original trilogy.
In Star Wars Legends Leia was visited by the force ghost of her father Anakin Skywalker, the man who used to be Darth Vader. It wasn't a pleasant meeting as Leia was unable to forgive him for the things he'd done no matter how hard he begged, and it was the only time she saw him.
There are few reasons for this; firstly, the young Skywalker has become more powerful. While he didn't continue his traditional training with Master Yoda, Luke was on the field, practicing what he knew thus far, and honing his skills in the real world.
Luke Skywalker is finally able to break through and help his father turn from the dark side of the Force, only for him to sacrifice himself and die moments later. Yet if Luke had somehow managed to keep Vader alive as the Death Star II collapsed around them, the future of Star Wars would change drastically.
The realistic answer seems to be, yes, Anakin in his prime could have defeated Luke Skywalker (in the current canon) if they battled one-on-one. The main reason behind this is Luke's lack of formal Jedi training, at least when it comes to combat.
Nope. Not one of Sidious's apprentices was stronger than Vader. And Maul himself openly admitted in Star Wars Rebels that he couldn't defeat Vader. So no,Vader wasn't a weak Sith Lord.
