I'm not sure weighting comes into play

That's the direction I'd head, I think. Each field contributes to the likelihood of a match, but probably not equally. If they are equal then you can just add them, right?

One way to solve this is with a neural network. You'll need a training set of known records with known-good result values. If your training data is good then your network should be able to assign optimal weights to the various inputs. If you don't have a source of good, diverse training data then don't bother going down this path.

-sam