Commanding is meant to create an obligating reason for another, while requesting is meant to create a non-obligating one. Promising is meant to create an obligating reason for self. There is a natural spot in illocutionary space, then, for a speech act meant to create a non-obligating reason for self, a speech act type that stands to promising as requesting does to commanding.
We would expect that when I have a normative power, I also have the corresponding weaker powers. If a legislature can bind under pain of ten years' imprisonment, they can bind under pain of a week's imprisonment. If I can create an obligating reason for myself, I can create a non-obligating reason for myself. That's another reason to think that we would have the "weak promise" speech act that creates non-obligating reasons.
I am not sure we have good phrases to express weak promises. We can approximate the force of a weak promise by weaselly promissory wordage like "I'll try to do this" or "I'll take your needs into account".