A former peace-seeking activist, Dr. Elizabeth Weir is fluent in five different languages (well, six if you include Ancient) and served as an international negotiator for the US government.
In Stargate SG-1 Season 7's "The Lost City," Elizabeth is placed in command of Stargate Command, replacing General George Hammond as a civilian leader, at the order of recently-elected President Hayes. Although pressured by then-Vice President Kinsey to get rid of SG-1, Elizabeth- demonstrating a strong sense of integrity and commitment to doing the right thing- goes against Kinsey's demands and eventually authorizes SG-1's mission to find Atlantis.
In Season 8's "New Order," Elizabeth continues her job as leader of the SGC. She approves Sam and Teal'c's mission to go find the Asgard, and she and Daniel attempt to negotiate a peace treaty with the High Council of the Goa'uld. Although used to making people see the truth rather than embellishing it, when dealing with the Goa'uld in her first intergalatic treaty, she picks up the skill of bluffing, and is actually quite good at it.
At the end of "New Order Part II," Elizabeth becomes the head of the research team at the Ancient output in Antarctica. She continues this role in Stargate Atlantis, the Stargate SG-1 spin-off series. In "Rising," she, Dr. Rodney McKay, and Dr. Daniel Jackson convince General Jack O'Neill to approve a mission to go to Atlantis, the lost city of the Ancients, located in the Pegasus galaxy. Although she knows that the trip may be permanently one-way, she nevertheless excitedly leads an international team of scientists, military officers, and others through the Stargate.
Generally calm and patient, in Season 1, she is still learning her place as leader of Atlantis. She believes that she can't afford to have or show any doubts, and her decisions always go back to what is best for everyone involved. Although she remains a bit idealistic in Season 1, she nevertheless makes some hard, morally questionable decisions. However, it's in Season 2 that she begins to make more extreme decisions that she probably never would have even considered in Season 1.
In Season 4, the producers got rid of Torri Higginson and so wrote Elizabeth out of the series. Her nanites, previously inactive as of Season 3, are reactivated to save her life, and then she appears to sacrifice herself to save everyone. Later, her clone says that the real Elizabeth is dead. However, we later see what seems to be the real Elizabeth leading a renegade Replicator group, so presumably the real Elizabeth IS alive and kicking. Somewhere.
In Season 1, back on Earth, Elizabeth left behind a boyfriend, Simon, and her dog Sedge. (Sedge, incidentally, is also the real life dog of Torri Higginson.) However, in Season 2's "The Intruder," the two break up, Simon having found someone else. (What befalls Sedge, we don't know.) She and Colonel John Sheppard, the ranking Atlantis military officer, sometimes clash; their relationship is also one of the more interesting ones of Stargate Atlantis, and despite their disagreements, their relationship is embued with a strong sense of mutual respect. As for Rodney, Elizabeth, in Season 2, states that she sometimes has to protect him from himself; Rodney, on the other hand, favors her a certain respect that he does not give to many others, and in Season 3, basically admits he has somewhat of a crush on her, or likes the idea that she has feelings for him. Elizabeth's relationship with Teyla is, sadly, not as developed as many fans would like; the two women are similar, both being leaders, and they seem to respect one another, but we do not see them together that often. Weir's relationship with Ford is even less developed - he is respectful towards her, but that is about it. Ronon Dex and Elizabeth's relationship can be described as "cautious" or "wary" - though Elizabeth sometimes tries to get to know Ronon better, he is usually rather reticient, not offering much of himself. In "The Long Goodbye," Ronon says that while he understands Sheppard, he doesn't have a clue how Weir thinks. Elizabeth gets along with Carson Beckett rather well. Her most tulmultuous relationship is with Colonel Steven Caldwell, though it's not known how much of this friction is (was) due to Caldwell being host to a Goa'uld.