The weight it adds is negligible. The piezo ribbon and cables might be couple of grams. The preamp is on the end pin jack, and the battery is on the neck block ... both are quite light and mounted in relatively non-resonant locations. If you don't use it plugged in, just omit the battery (which is by far the heaviest component).
At the very least you'll have to shim or replace the saddle. Of course, this involves a quick set up to get it right.
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