Not to be fair, but to be thorough.

On the subject of Weir, I have mixed thoughts. Let's stick to the multiple point format.

• I find her appearance strangely off-putting.
  
• I rather liked her, in Season One. Season Two, she seems largely immoral or demented, but then so does everyone else. I really enjoyed that she didn't wear makeup at first, and want her to slouch around her quarters in sweats, doing funny-looking yoga.
  
• There is no desire in me to read about her having sex , in the graphic sense, but I want her to have many enjoyable affairs with hot aliens in canon. Love 'em and Leave 'em Weir. Really hot ones, too, not just tolerable. Hot like Ronon and Teyla.
  
• She can be incredibly heroic. I admire her moments like that, a lot.
  
• Watching her wrangle with Sheppard always reads to me as about power, not sex, and I LOVE LOVE LOVE that, so much. Those are some of my favorite scenes in the entire series, even including McKay's moments and Ford's gorgeous shiny grin and the whoosh!ing ships.
• I want her to be one of the lone wolf leaders, standing tall (metaphorically, hee) and alone, with hard decisions making firm lines around her mouth. I want her to be tough, and negotiate the hell out of the P. Galaxy.
• Her behavior toward Kavanagh was appallingly bad leadership, so sad. Had a hard time with that. I'm not just talking about The Incident, either. 38 Minutes made her look pretty poor at guidance to me. She wastes resources, especially personnel.
  
• I wish they'd give us more scenes between Weir and Teyla.  I want to see them bond. And argue, but with respect.
  
• For some reason, Elizabeth/Ronon works for me, every time. They fit, in that they really shouldn't. But her bemusement at him is charming.
  
• I'd award her as a prize for adorableness to Zelenka, but. I don't think she's going to go for him.
• Sheppard/Weir/McKay, if only the gen version, is the heart and soul of the show. But the show isn't as good because of it, since it is absolutely stupid, criminally stupid, for her to go on missions at all. If she got to have more unfortunate accidents with ancient technology, though, it could be much more fun.
  
• I think maybe I still kind of like her. Creeps me out, though, after Michael.
• I find it very easy to feel like I understand her.
• Of all the characters, she's the only one that gets a pass for the idiocy surrounding the Gilbert Ryle episode.
  
• Watching her shoot a gun does nothing whatsoever for me. She has a lot of power, without the need to run around and play soldier. I like watching the few scenes where we see her negotiate seriously the way other people seem to enjoy the gun scenes.

As far as pairings go, and in fiction, I can see a wide variety of possible Elizabeths. My favorite het versions pair her with Ronon, or McKay, or Zelenka. Sheppard/Weir het isn't my cuppa because I really like to read them as mutually supportive political animals, with underlying struggles and tension which is about will more than sex. It's how they naturally occur to me, and is fun. (See Crimes against Humanity by seperis, for a perfect example of the sort of interaction I like between them. Or maybe Three Fates, which has them as more than friends but the power struggles are still there.) Weir/Teyla stuff would work, except I like them gen too, usually.  But really, I like Elizabeth gen most of all. Lone wolf! Leader of the pack! High and lonely destiny! She'd be cool Ascended, too.

If the writers loved me, she would be a great leader, make wise choices, and take names in Pegasus. And they'd let her fall prey to some more Ancient devices without having to be stupid to do it. And maybe be mind-wiped and think she is the reincarnated great leader of some people that keeps bisexual harems on a planet with an excess of silken pillows. Because, how fun would that  be? It'd be much fun, oh yes.