.01% resolution is pretty tight. In theory that's 14 bits, but you will need 16-18 (or more) because of noise and other errors. You will need a precision reference of the highest quality and calibrate the system regularly.
I don't know of any available shields with higher accuracy ADCs, but they can be made pretty easily as in the links below.
http://forums.adafruit.com/viewtopic.php?f=31&t=12269\
http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1261408885
You can gain some accuracy by oversampling and changing the reference, but you probably won't get .01% using the ADCs on Arduino.
IMO your best option is to get a scale with a serial port and read it digitally. The OEM has done all the critical design work and you can buy as much accuracy as you can afford.
A scale with RS-232, or one that can be hacked to intercept SPI or I2C would be the easiest. If you get a USB scale I don't know if the Arduino can be a USB Host, but I've not done anything with USB. Hopefully others can enlighten us, or ask in the other forum categories where they may be more familiar with the issues of USB interfacing.
The simplest, though not the cheapest, solution may be use a cheap, old PC to host the USB and a simple program (Python, Visual .NET etc) to read USB and pass instructions over serial to the Arduino which controls the robot movement. If you need any heavy duty calculations or lots of memory, it can be done on the PC as well.
Steve
P.S. Please post more details about your project when you have it. I imagine it is some kind of sorting operation which might be similar to a future project of mine to sort spent cartridge brass by weight, length and possible other factors (caliber, headstamp, brass/nickel/steel, split/damaged etc.). I am an EE, so the electronics are pretty straightforward, but I need a brilliant idea for the mechanical handling side of things that doesn't cost a fortune.