Fill it with water with a plug in it at home with a garden hose.
If there’s no leaks, put the hose to the bilge pump out let. That would be my first guess. A rivet leak usually isn’t terrible unless it is multiple rivets that are completely gone. I’ve had both issues. Plus helped a friend with plumbing issues where a live well pump and hose had froze. That sucker leaked like a stuck pig. But that shouldn’t be affected by weight, that would be constant. The weight pushes me to think it’s a bilge exit port or splash well/transom issue. I would highly doubt it’s a plumbing issue, but you never know.
Keep us posted, I’m curious what it is.