Jayne is not a man much given to introspection. In his opinion, if you can't fight it, screw it, spend it, eat it or drink it, it's probably not worth much. That's why he's the tank. That's why he's always been the tank.
Sarie confuses him.
She falls into none of his categories, respects none of his limits. She fears him not at all, which is a definite departure from his previous experience. And for some reason, she refuses to see him as anything more than a giant teddy bear. And he, for some equally unknowable reason, lets her.
He doesn't understand that, and contrary to popular belief, Jayne is not used to not understanding things. He may not take the subtle approach his crewmates seem to appreciate, but that is because he is a simple man with a simple life. Confusion over a little girl he could probably toss halfway across the 'verse doesn't fit his uncomplicated worldview.
So he doesn't think about it. It seems like a good solution. Eventually he places her in the same category as her mother. Both itty bitty things, with big smiles and happy natures. Uncomplicated. Like him.
Maybe that's why he likes her.