It depends on your supply chain. If you only have a handfull of suppliers, OR if you are in a supply chain that already uses these types of compliance labels, OR if you happen to be Wal-mart, you can probably make it happen.
You should first talk with your suppliers to see if they are already doing some type of compliance labelling for other customers that include the pallet weight. It may be that there is already some compliance labelling going on in your industry and your not getting it because you didn't request it. If so, see if these meet your needs and then just ask that they be included on your shipments.
If not and you need to start from scratch with your suppliers, you should first review all your requirements so that you don't have to keep going back to suppliers in the future asking for more stuff.
Also be realistic about what you expect from your suppliers and make sure you are actually going to use them. Don't make your suppliers do this only to find out that you don't have the discipline to make sure your workers use them, or that you don't really need them.