Even though the A/D is 10 bits, you won't get a lot of accuracy unless you have a dedicated Vref and you average a lot of readings. You might get 9 bits of accuracy in that case.

You can do a lot better if you amplify the signal with a rail-to-rail input / rail-to-rail output op amp.

If you don't want to go that route, you are going to have to get a bigger voltage change than you will get with your setup. First, R1 will have to be smaller than 10K. I don't know how many "ematches" you plan to have, but 330 ohms would seem to be a good value. Of course, the resistor would have to be a 5W type. This will give you 72mA through the resistor, and .218V across 3 ohms. You will also need a 2K 1/2W resistor between the junction of R1 and R2 and the PIC input to protect it when the switches are open. That should give you enough signal to work with.