I could see the events of the BDM really changing their relationship. In the series and in the movie, it’s clear that Jayne actually fears River. Unlike everyone else, he never really sees her as the sweet little girl. He understands completely what she is capable of. I think after the events of the movie, though, that fear would develop into more of a respect. She literally killed Jayne’s greatest fear. I could see that relationship developing really nicely with Jayne respecting her, and them working together, becoming friends, and then more. I could also see the rest of the crew, despite everything that happened and despite the fact that River is more lucid now, still sort of treating her like the kid sister of the ship and still worrying over her more than necessary, and Jayne wouldn’t so that. I can really see Jayne being the only one who truly recognizes everything she’s capable of.
Plus, Jayne loves his weapons more than anything and what is River? The perfect weapon.