In this case why not just divide the estimate by the confidence to get the "true estimate" e.g in your example it's actually a 4 week. If you provide a tuple the confidence will eventually be conveniently dropped in some slide deck then the "2 weeks" will be socialised as the commitment.
The estimate-confidence relation is not linear. In my experience it follows some kind of S-curve, with 0% confidence approaching impossibly short times and 100% approaching infinity (like a logistic function).
I think software projects are best estimated as gamma distributions. To express that as confidence levels, you use the cumulative distribution function of the gamma, which are kind of S shaped, but stretched to the right.
