As someone has said, the WNA marking is mainly related to weather and is
applied to ships below a certain length above a specific latitude. The
basic idea being to allow some minor additional freeboard as a safety
factor.
There are a number of these draft markings, all the way to Tropical
Fresh which are mainly used when loading at a specific locale and going
to another, to give you a basis as to how deep you can load, as you
can't be below the draft requirements at the next port.
Regarding markings on the side of a barge ..... I've never seen any
denoting displacement, however, reading the draft is a quick and easy
way to know how much cargo (weight) has been loaded.

otn