I think you're succumbing to the temptation to think of the DMG entry as describing an item, rather than describing an aspect of an item. It's really not so much Mariner's Armor as Mariner's Chainmail, Mariner's Plate Armor, Mariner's Studded Leather Armor, etc., and they're just listed as a single entry to save space. Check out the DMG p. 139:
If a magic armor doesn't specify its armor type, you may choose the type or determine it randomly.
In other words, "Mariner's Armor" is just an enchantment that can be applied to any kind of armor to make it grant a swim speed. Unless you really want the seashell decorations to weigh extra, it weighs whatever the base armor would weigh. (Aside: that's also how you know the AC, by looking at the entry for the base armor.)