Submitted by a Dododex user:

"The mining drill reduces weight when it's equipped. This can be really handy, especially when riding a tame that allows it to be equipped. For example, the magmasaur doesn't do weight reduction on stone and wood, but if the mining drill is equipped these materials can be transferred to the player's inventory for the weight reduction. Another place where I find it really useful is when mining metal and transporting it with a skiff -- if the metal is dropped onto the ground using the O key (one package at a time), the player can pick up as many as there are inventory slots, and with the mining drill equipped the player can fly the skiff with much 4x the metal that the skiff itself would hold.

I just double-checked the mining drill on some basic materials, and it seems to be a 75% weight reduction for metal ore, stone, and wood. I don't think it reduces the weight of anything else.

Attached are screenshots of that test, with and without the mining drill equipped. I forgot to include crystal in that test, but I'm certain that the mining drill does not reduce its weight."