What version Zen Cart? Look in the Tools ... Server Info ... for the exact version ...

What Shipping Modules are installed?

Do they have zones?

Does 0 weight mean Free Shipping? If so is Free Shipping freeshipper installed?

If not, turn that off in the Configuration ... Shipping/Packaging ...
Order Free Shipping 0 Weight Status
If there is no weight to the order, does the order have Free Shipping?
0= no
1= yes

Note: When using Free Shipping, Enable the Free Shipping Module this will only show when shipping is free.