As Leia did not discover that she was a child of a Jedi until ROTJ, she would not have been able to intentionally use it. She also did not have any training so her use of the Force would be limited compared to other people who had been trained and studied it for years.
Fans know that the princess did not have Jedi training when she appeared in the original film trilogy; however, she does show Force sensitivity in these films, most notably in her ability to mentally connect with Luke — and in the expanded universe, she eventually did become a Jedi.
Why did Vader sense Luke but not Leia? He only senses Luke when he actually using the Force, Leia is not actively aware or using the Force and therefore he does not sense her. He is also not looking for a daughter either until Luke spills the psychic beans on her later on.
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 never used the Force in the original Star Wars trilogy but was seen using it in Star Wars Episode VIII: The Last Jedi to save herself from certain death. It was also revealed that she received Jedi training from Luke but refused to be a Jedi because she feared what it did to Darth Vader.
Padme didn't have any force powers and she was too old to become a Jedi. She may have had some kind of force powers whilst pregnant with Luke and Leia but being with Anakin could have caused some force sensitivity at the time.
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.
She was too well known for a start. The daughter {highly unlikely it was common knowledge she was actually adopted} of Bail Organa, a Princess of Alderaan and a Republic Ambassador. Pretty difficult for Obi Wan and Yoda to train her as a Jedi without it getting out.
In short: He felt Luke wasn't ready. Yoda was the grandmaster of the fallen prequel-era Jedi Order and trained Jedi for centuries, with students typically beginning as young children. He saw too much of Anakin in the young adult, and he didn't want to end up training the successor to Vader.
Nope. Luke, unlike Leia, never really had a father figure in the first place. Leia never was saved by Darth Vader the way Luke was, and never understood Luke's forgiving him. She hid her identity as Darth Vader's daughter, and identified as Bail Organa's daughter.
Abrams says Princess Leia chose not to train in the ways of the Force. In the films, while Luke trains to become a powerful Jedi, Princess Leia is kept busy by essential duties of her own. Later, as the leader of the Resistance, General Organa has her hands full with tasks that don't involve any use of the Force.
Miramir had a Force-sensitive child with Dathan, a daughter named Rey, who was born in 15 ABY. Though Miramir's husband lacked the ability to use the Force, Rey was born Force-sensitive as a result of her father's genetic connection to the Palpatine bloodline.
Love triangles and awkwardness — The Empire Strikes Back wasn't the first inkling that Luke and Leia had feelings for each other. Their romance was heavily alluded to in A New Hope, what with all of Luke's suggestive facial expressions to Han whenever Leia was around, and Han's clear attraction to Leia.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
So, Yoda decided to spend time away and rejuvenate his connection with the Force. Yoda's decision was made on the basis that if Luke and Leia were meant to become Jedi, the Force will guide them on their way!
However, Luke knew Leia at this time, and Yoda knew they were siblings. He wouldn't tell Luke until the next film that there was another Skywalker, but why wait when he had the potential to train two at once?
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.
The first time, Obi-Wan tells Leia she reminds him of someone “fearless and stubborn,” a “leader who died a long time ago.” While it's possible he was referring to Satine Kryze (voiced by Anna Graves in the Clone Wars animated show), it seems more likely he was talking about Padme.
With Leia, Luke, and Darth Vader all being major characters in "Obi-Wan Kenboi," the show is having to tread lightly as the "Star Wars" canon is pretty explicit. We know exactly when Vader discovered that Luke was his son, and we know when he figured out that Leia was connected to him as well.
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.
Jedi had especially high midi-chlorian counts, and of them Anakin Skywalker was said to have the highest ever recorded at over 20,000, even higher than the powerful Jedi Master Yoda. Though Skywalker later lost a good deal of his organic body, his cells continued to teem with midi-chlorians.
That said, both Yoda and Yaddle have a high midi-chlorian count in their blood. Yoda's m-count was roughly 18000, while Yaddle's was closer to 12000. It is reasonable to assume that whatever species they are a part of, it is a deeply Force-sensitive one.
To be categorized on the first level, or the "normal" level, of midi-chlorian count, one would need to have around 2000 - 2500 midi-chlorians per cell. A person with a midi-chlorian count this low would likely never experience a call to the force or realize any abilities.