How strong is this obligation? An argument for consequentialism from concomitant variation

The rule ‘Keep your promises’ is often presented as a challenge to consequentialism, because the ground of your moral obligation not to break a promise seems to lie in the past fact that you made the promise, which is not a consequence of the act. A different picture emerges, however, when we move beyond the question of whether you have any moral obligation at all to the related question of how strong that obligation is.If I promise to meet you and some other mutual friends for a casual lunch, then my moral obligation to meet you is not as strong as when I promise to drive you to the airport to catch an important flight. Why not? The natural answer is that, if I break the lunch promise, not much bad will happen. You will still have a pleasant lunch with our other friends, and you and I can still have lunch some other time. I have some moral obligation to meet you, but not a very strong one. In contrast, if I break my driving promise, then my failure will cause much more harm, assuming that you will not find another way to get to the airport in time for your flight. These harmful consequences to you seem to be what give strength to my moral obligation to keep this promise.The relevant kind of strength is measured by how much is needed to override the obligation. I would need much stronger reasons to justify breaking my promise to drive you to the airport than to justify breaking my promise to meet you for lunch. The fact that my teenage child is sick at home might be enough to justify missing the lunch, even if the teenager would be safe at …