Sounds oddly familiar to me! This is really the only exemption I could find right off the bat, it's been awhile since I've dealt with label regulations since I now work for a co-packer so all of this stuff is done for us now!
(3) Individual serving-size packages of foods containing less than 1/2 ounce or less than 1/2 fluid ounce for use in restaurants, institutions, and passenger carriers, and not intended for sale at retail, shall be exempt from the required declaration of net quantity of contents specified in this part.
I would try to ask the customer why the net weight can not be included and explain that according to label regulations by the FDA, anything over 1/2 ounce needs to declare net weight. Then from there determine if you still want to package their product.