The stone bears on a footing, not the wall.

Your foundation will need to support the stone.

Are you thinking of using stone adhered to the exterior? Look at the pecs provided by the manufacturer, but it should work.

Yes the stone is adhered to the exterior wall - the foundation will have added footers for the weight too.

Natural stone, probably not. Thin cultured stone that will look the same, probably yes. Details to consider.

It’s natural stone veneer - 1 to 2 inches thick pieces

I’m not weighing in with advice, as I have no idea if it can be done in your situation, just thought I’d share this old thread for interest:

https://www.houzz.com/discussions/198849/we-just-gave-our-60-s-bungalow-a-complete-facelift

Obviously, you need a qualified pro to assess it all in person.

You don't need foundation support for adhered stone. It's done all the time. That's one reason it's so popular. Search for "Adhered Natural Stone Veneer Installation Guide".

Seabornman - this is exactly the installation we are looking to do - thank you.

https://naturalfacing.com/wp-content/uploads/2017/12/NF-Adhered-Natural-Stone-Installation-Guide.pdf

Questions I have are can the foundation or the exterior framing support the weight?

The movement inherent in a framed wall is a concern, not weight, per your linked instructions.

"Good way to water damage your home."

Not if you install the stone per the manufacturer's instructions which clearly require a moisture barrier at the face of the backup wall.