Generally, he weighs the most. In this situation the heaviest party tests the bridge because if it’s safe for them, it is for everyone else in the group too.

From there it just becomes tradition.

Though I agree, in your exact example probably the woman should go first but only because there’s no other way down and if there were any children in the group they’d be unlikely to brave enough to do so, depending on age.

Ha! The kid issue may be where the tradition started! Imagine …

A family in the same situation. The kid is freaked and clings to Mom making their combined weight the largest. The freaked out kid is also freaking out all the other kids. So Dad goes first to distract them enough from causing a more severe problem and also show the older ones it’s safe so they’ll cross by themselves. Leaving Mom and the first freaked out kid or youngest kid to cross last as the heaviest.

As I said, it becomes tradition. Nobody remembers why. But yeah, Dad keeps the kids at pace and makes a game of it so Mom doesn’t get swamped with terrified kids in a potentially dangerous situation.