Tame a doedic pump weight then set it on wandering and pick it up with a argy and fly next to a rock and it’ll collect stone. Since the doedic has a weight reduction you should just leave it in his inventory.
On PS4 I tried to test it's obsidian gathering since it is "Rank 1", well all it was gathering was stone. So I went to another saying maybe something was wrong, NOPE it does not gather obsidian. Just use an Anklyo for that.