The heavy chest can be obtained as a reward from master reward caskets, which are obtainable by completing master clue scrolls. It has no stat bonuses and is purely cosmetic. Carrying the chest will also change the player's idle, walk, and run animations.
Chest (Barrows) - OSRS Wiki
Barrelchest, Old School RuneScape Wiki
Treasure chest (Carnillean Rising) - The RuneScape Wiki
Chest (50 coins) - The RuneScape Wiki
Trawled through the revision histories of the RuneScape Wiki to bring you the stats of Nex's ancient armour drops, all in one place. : r/2007scape
The Everlasting, Old School RuneScape Wiki
Giant Mole, Old School RuneScape Wiki
Update:Thok's Smashing Buffs - This Week In RuneScape - The RuneScape Wiki
Bosses - The RuneScape Wiki
Locked chest - The RuneScape Wiki
Update:Spring Festival & Frank's Free Chest 2 - This Week In RuneScape - The RuneScape Wiki
Evil Chicken, RuneScape Wiki
Muncher - The RuneScape Wiki
Cosmetic chest - The RuneScape Wiki