I've been thinking about relationships on Primeval, particularly the two "standard" ships starting in Series 4 (thought one has been a long established relationship).
Let's start with my take on Becker/Jess: Jess definitely has a crush on Becker. There are NO doubts about that. But I don't see any reciprocation. I am sure that many would say, look to series 5 when she is hurt by the beetle, and I have. I don't see it as a romantic reciprocation. First of all, he is charged with ARC security. She was injured at the ARC. He failed to protect one of the team, so in his mind he's going to worry. He was there to see the loss of Nick, the year long loss of Abby and Connor, the longer loss, regain, and loss again of Danny, plus he blames himself for Sarah's death. That's gotta weigh on a man. Becker, imo, sees Jess in the same light as he would a younger sister. She's the youngest of the group, probably the most vulnerable in his mind. She's not out in the field like Abby or even Emily, she's the tech person in the ARC. Also, she was bit after they lost control of the beetles because *he* killed the Queen. Guilt, guilt guilt.
So... yeah. I see Becker and Jess having a brother/sister relationship- once she moves on from that crush of hers. I don't see Becker reciprocating her feelings. Could he eventually? Potentially, but I think the chemistry and interaction was too forced. Ben definitely played Becker as being a bit uncomfortable with the attentions Jess gave him.
On to Connor/Abby: Of my ships, this one has moved down to the lowest on the totem pole and rarely is a factor for me. My thoughts as to why are a matter of growth. One thing I've noted about Connor is that his character has had very little change, imo, over the evolution of the series. He's gotten a little harder, what with being there for the loss of Stephen and his own mentor, Nick, but I don't feel he evolved as much as Abby did during that year in the Cretaceous. Yes, he evolved some, but I feel that once he was back home and working in the ARC, specifically with Philip, that he almost seemed to go backwards and became more of the Connor we saw in series 2, beginning of series 3.
Abby, on the other hand, has definitely evolved. She has gone from being the spunky, tomboy, lizard-girl, to being a much more mature, centered individual. She's an integral part of the team, without worry of actually handing her a weapon and putting her in the fight alongside Matt and/or Becker.
I think that's why my brain has started shipping Connor/Jess, because they seem to fit better in terms of personality and maturity level. Abby does love Connor, but I see it changing from the physical love they have shared into something... not necessarily less, but different. Almost as if she's evolving out of a "young" relationship and is in need of one more "mature" and withstanding. If that makes sense?
I do think that she could have had that with Stephen. It was obvious in series 1 that they seemed to be the route the writers wanted to go (especially seeing the promo shots that were done now), but I think between James Murray's leaving the show at the end of series 2 and the RL relationship between Hannah and Andrew, the writers decided to go the Abby/Connor route instead.
I know a lot of people, pre-series 4/5, ship Connor/Abby, Becker/Sarah, but I gotta admit that Sarah had a lot more moments with Danny than she did with Becker. Once Sarah was gone, it was *way* obvious that they introduced Jess as a love interest for Becker. Maybe I just have a thing against forced relationships. There's only a few canon relationships that I have rooted for since day one. I have a tendency to be in the minority and ship the unusual ships or the "OMG WHY?" 'ships. It's rare for me to pick a popular one, or what some fandom people say is the "right" one.