Wesrock:
It being the greatest should in now way change the burden of proof.
Depends on the claim actually. If we were standing outside and I told you there’s a molehill a mile north of us, you may believe me. Especially if there’s moles in the area, if you’d just seen me walk back from the north, and ultimately because the claim is fairly benign, there seems no motive for me to lie about the molehill and it doesn’t seem to affect your life one way or another.
If on the other hand I claim there’s a mountain a mile north of us when you can’t see one, you may be more skeptical. A mountain a mile away should be clearly visible to you. You’d expect there to be … well a mountain.
If I go further and claim it’s an invisible mountain, that I just climbed to the top of and at the top there’s a box and inside the box is a paper upon which the creator of the universe has written his favorite chili recipe … well you’re going to tell me to have a nice day and quickly walk away because you’ve run into some nut who’s trying to ruin your nice walk through nature.
This is the old ‘extraordinary claims require extraordinary evidence’ idea. So yes the metaphorical ‘size’ of the claim does change the burden of proof. The less the claim appears to comport with reality the more evidence we generally expect. This is the standard we use for almost every claim we come across outside a religious nature.