It would depend a lot on the creatures holding the rope and the one falling but for the most part i would ask for a strength check, even if the characters could normally carry that amount of weight.
This is because the momentum of the falling character will mean that more strength is required to stop it falling than it would to lift it in the first place.
I would ask for the strength checks starting with the player first player holding the rope. If they pass, then nobody else needs to make a throw. If they fail the check by less than 5 then the next player makes the same check with advantage as some of the weight is being held. If the first player fails by more than 5 the next player makes the check normally as the first player loses their grip on the rope. If they fail by 10, or critically fail, i would say that the player is pulled over the edge and then move on to the next player who makes the saving throw but with a higher DC and so on.
This adds the risk that I think you are looking for and forces them to consider the order in which they cross the bridge carefully.