Breaking ribs during CPR or breaking legs jumping are different scenarios: the rescue effort is directed at the same person suffering a double effect. Here the fat woman gets an injury before she dies, and the injury is direct result of a freely undertaken act of the firefighter.
I suppose you can say that the injury can be neglected in comparison to death, if it is merely a risk of injury. However, I still don’t see pushing her to a sure injury. It could the the case where the mind of the firefighter simply cannot contain the amount of faith in God necessary to consider the situation intractable. But still, the moral ideal is to leave the situation to God and not push the women; the situation, in truth, is intractable.
So do we have a recognized Catholic moral theologian opine on this?
I’m not sure to whom I’d turn.