Ramban there offers a couple of reasons:
Leah's eyes were weak (29:17), so the sun would be harmful to her.
Precisely because she was older, so there was more of a concern that the shepherds would take inappropriate liberties with her.
This much is definitely true: The chevra kadisha Prushim in Jerusalem does not allow a son to carry the body of his father from the funeral home to the hearse nor from the hearse to the grave. I read about it in this article and experienced it first hand. The explanation there is:
descendants of a male deceased will not participate in the funeral ...