Some places wont insure a roof unless the old asphalt shingles are removed.
^^^^^
I know of contractors that will not warranty the work or the material's if they are installed over any other roofing material.
Why?
Because it means warranting materials you did not install, and labor you did not provide. That previous roofing material is already compromised, or it wouldn't need repairs. It may sag, swell, shift, buckle, or separate, dragging the new material with it, causing issues that the roofer will have to fix. It's a simple case of avoiding a possible problem later.
As for the weight issue being a myth, that is not true. It varies from place to place, but either 3 or 4 levels of shingles is the max for a "nail over".
I grew up in the construction trade, worked as a roofer, carpenter, punchout man, drywall, masonry, I ran one of two crews for a general contractor.
Something not mentioned is the pitch of the roof. That has a great deal to due with the acceptable load on that roof. You will note that areas with high snow fall, also have sharply peaked roofs, so the snow load does not collapse the roof. (Helps to have an Engineer for a father)
I, personally, will not do a "nail over", even if they are legal for a couple of layers. It's half-assed, it does increase the roof load, and it does not expose problems with damaged or rotting roof members or sheathing. (You can't see it, so you just don't know. )
I would suggest doing the tear off, and examine the wood beneath, correct any issues you find, then reroof.
