try this:
http://en.wikipedia.org/wiki/File:Op-Amp_Non-Inverting_Amplifier.svg
http://en.wikipedia.org/wiki/File:Op-Amp_Inverting_Amplifier.svg
You would connect the output of your hall device directly to the input of one of the above.
The gain is given by the ratio of the two resistors in the second case and almost the same in the first.
If you had a voltage change of 0.2 volts in each direction and wanted 1.5 volts in each direction, you would want a gain of 1.5 / .2 or 7.5.
So, you might choose 10 K for the input resistor (or R1) and two 150 Ks in parallel for the feedback resistor (or R2). You need a plus and minus power supply for this op amp and also for the Hall device. The Hall device would require +/- 2.5 volts. That is 4 power sources.
I'd still use a Picaxe chip. You can have PWM out of the same picaxe to give an analog readout if you wanted.