Every knows that Jessie has the absolute hots for Cloud. She's all up in his grill, touching his face, making him special fake IDs and whatnot.
But when Elmyra has her little flashback, we clearly see Biggs and Jessie hugging and trout at the Sector 7 train station. What is the meaning of this!?
There are a variety of options here. Firstly, the crap option, which is that Square just recycled their models. Lame. That's not what really happened.
The second option is that Jessie is a huge flirt, and is keeping Biggs around while she tries to pick up Cloud. Far more believeable, and hey, he's acharmingmuscular guy so what's not to love?
Lastly is the idea I favour most, and it is that Jessie and Biggs had a romance which turned sour. They instead turned their hate and resentment towards each other into motivation to work hard for AVALANCHE. etc etc I could create a wicked tale here but I'll leave it to you to tell me which is right, or if you have another theory altogether!