Obiwan watched over Luke instead of Leia because Bail Organa offered to take Leia which put her in a relatively safe situation. She was a princess for Alderaan which was a wealthy world. On the other hand, Luke was being raised by his aunt and uncle on Tattoine. As moisture farmers, it was very different than royalty.
Obi-Wan Kenobi's biography on starwars.com states that he chose to live on Tatooine specifically to watch Luke as if he had always intended to train Luke and not Leia. It seems that Luke had the advantage as he lived only miles away from Obi-Wan while Leia lived in an entirely different star system.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
Obi-Wan wanted to protect Luke
The news that his father was in fact a Jedi Knight who had died during the Clone Wars was a lot to take in itself, but still less severe than learning that your father had turned to the Dark Side, brought about the end of the Jedi Order and become the most feared man in the galaxy.
Yoda may have wanted to train Leia instead of Luke, but he was wrong - precisely because he did not understand that the redemptive love of a son towards his father was what would bring balance to the Force. Fortunately, the will of the Force won out, and Luke was the one chosen to train as a Jedi instead of his sister.
Now that she knew the truth about her parentage and her Force powers, Leia trained as a Jedi with Luke, honing her Force abilities and constructing a lightsaber. But she ended her apprenticeship after having a vision that her Jedi path would end with the death of her son.
Leia's journey yields a time dilation of 62.6 days; however Luke experiences a time dilation of 700.8 days (1.92 years). The students concluded that Luke is therefore 1.75 years younger than Leia, possibly rendering them the first twins ever to have over a year between their ages.
R2-D2 was in on the scheme to keep the secret away from Luke and Leia. He was devoted to the Skywalker family, and at the guidance of Obi-wan and Yoda, he would have maintained that secret in order to help protect the twins.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
It's the kind of extra and flamboyant gesture that the Jedi seemed to love, but perhaps Obi-Wan felt that this grand gesture of sacrificing himself to the Force would give Luke (and Leia, and Han) the push needed to take his training seriously, and show him just how powerful a Jedi could become.
In Death Star, it seems the Sith Lord could have discovered Leia's true identity if he'd pursued his hunch. However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter.
Darth Vader only learned he had a daughter in Return of the Jedi - but there's no evidence he realized she was Leia before his death and redemption. 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.
The reason Darth Vader could sense Obi-Wan and Luke was because of how they actively used the Force several times throughout the Original Trilogy. Vader never sensed Leia because she didn't the Force; Leia did not even know she had Force powers to begin with.
Obi-Wan came to the Death Star to save Leia from the Empire's clutches, but was killed by Darth Vader while the others were busy escaping. Leia didn't see Obi-Wan again, nor did she experience any sadness when she learned of his death.
But it turns out that he was originally far more interested in training another: Luke's twin sister, Leia Organa. In the chapter “There is Another” in From a Certain Point of View, written by Gary D.
But when little Leia realized Obi-Wan had known her birth mother, he shared a story that not only made Leia's memories of Padmé plausible, it made them all the more moving. Jedi took babies from their families at an age when no child can retain memories.
After the battle, R2-D2 and C-3PO were the sole witnesses to the marriage of Anakin Skywalker and Padmé Amidala in Lake Country. After this Padmé gave ownership of R2 to Anakin while she kept 3PO.
Anakin wasn't "too old" because children were more adept at learning the Force — he was too old because he already had attachments to the physical world. Thus, Anakin couldn't properly be indoctrinated like other Padawans because he had knowledge they didn't.
Ironically, the truth about Luke wouldn't have gotten out if it wasn't for Emperor Palpatine. It was clear from the beginning that neither Yoda nor Obi-Wan Kenobi intended to tell Luke the truth in the original trilogy. Emperor Palpatine told Darth Vader that Luke was his son in Empire Strikes Back.
Leia wasn't really in love with Luke. She just did that to shut up Han Solo who was flirting with her on the falcon. Nothing ever came of it and it was never discussed ever in the saga's future episodes.
Not only was Leia incredibly strong-willed, but she also had the blood of the Chosen One coursing through her veins. This knowledge, paired with some more recent lore tidbits, suggests she was one of the most powerful Force-users to exist, perhaps even surpassing Luke.
There are clues in Star Wars to suggest that Luke and Leia did, in fact, know vaguely about their relation to each other much earlier than Return of the Jedi, but perhaps, were not yet Force-sensitive enough to have the full picture. One clue comes in The Empire Strikes Back when Luke is clinging for his life.
Affiliation. After discovering she was Force-sensitive, Leia Organa Solo utilized several lightsabers through her career as a Jedi of the New Jedi Order.
First, she admitted that she didn't really care about the Force. Thus, if she went with Luke, she would be doing it for the sake of being with Luke, not because she was following the will of the Force. However, more importantly, Leia refused to be a Jedi because Darth Vader's power had scared her.
Leia Organa-Skywalker
Leia Amidala Skywalker (portrayed by Carrie Fisher) is the wife of Han Solo, the mother of Ben Solo, the younger twin sister of Luke Skywalker, the daughter of Anakin Skywalker and Padmé Amidala, and the granddaughter of Shmi Skywalker, raised by Bail and Breha Organa of Alderaan.