One of my players got some heavy Mariner's Armor (DMG 181) last session.
We're playing in a game where encumbrance is tracked periodically, and since she ended up with a "heavy" variety I think that's all the more important.
According to the PHB, heavy armor varies from 40-65lb, but there is nothing in the description of the item that indicates the exact weight.
Best Answer
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:
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.)