Well, from the info you've given it's like the blind leading the blind. I can't tell you what to do next as I don't know where you're heading, or where you're coming from.
Instrumentation opamps are good for amplifying the outputs of bridges. From the sounds of your accelerometer, there's an amp built in, with scaling. I suppose if you are looking for a bipolar output (+ and -), the plus could be tied to the output, and the minus to ground, or even the opposite.
1) what part number accelerometer are you using? What is the power supplied to it, and the output's max (one direction (positive) or plus and minus?
2) what is it feeding? How are you going to record/measure the output? Just to add gain for gain's sake is not very efficient. If you are reading it with an ADC, you could just as easily scale down your reference and get a bigger reading without adding another gain stage. Each stage adds errors. Are you just trying to read the output on a voltmeter? Have you tried it?
3) are you going to calibrate the amplifier errors out, or are you trying to design something that is accurate to the nth degree without calibration? And what would that nth degree be? What sort of accuracy are you looking for, 5%, 1%, .1%? What is the accuracy/rating of the acclerometer part you are using?
4) what are you measuring with the accelerometer? Maybe 1000mV/g will overrange in your application, so no further gain is needed. How did you come to the conclusion that the acceleration isn't very much? Have you tried it? Have you measured it?