I have a home with 2x6 floor joists 48" on center and 1" plywood supported by concrete and 4x6 pillars spaced 6 feet apart. I am installing stone (marble) floors in two bathrooms which should meet L/720 deflection requirements. Is it possible the National Building Code in 1972 allowed 2x6 floor joists 48" on center? What should I do to improve my subfloors for the stone? Thanks

No code that I recall in 61 years called for 48" OC joists. I am sure I could help but I think you actually need a structural engineer to evaluate your home or maybe an architect.

You can verify this with an acrhitect or engineer, but if you install 2x6's perpendicular to the 2x6's you currently have, the 4' span would be well over the L/720 deflection, bringing you up to around 850. My concern would be the bearing strength of the 2x6's spanning th 6' distance. While you might be OK, you would definitely be OK if you sistered 2x6's along side each of the original 2x6's that you have there now. After that, no problem. I normally see posts about framing like this from folks in the northern reaches of CA to the pacific NW. They also normally have 2x6 t-g planking across the framing and most often the beams are 4x6, not 2x6.

The changes I suggested effectively turn your joist system 90 degrees and place them 16" oc. Underlayemnt rated plywood, oriented so that the long edge crosses the joists, not the 2x6 beams, overlayed upon your existing subfloor, using no less than 1/2", screwed only to the subfloor and not the joists, then install your cement board or membrane. If your 1" of plywood is multiple layers, post back. It might change the prepe ou need or cahnge the suggested thickness of underlayment. For example, if you have 1/4" ply over 3/4", then the 1/4" must go. No 1/4" ply under ceramic or stone, ever. That would change you to needing 3/4" underlayment.

Once you change the direction of the joists by adding the sisters and installing the 2x6's, since you've changed the existing plywood subfloor to being oriented in the wrong direction.

you should easily cut out and remove the one inch sub with 4 oc and replace with at least 2x10s 16oc all you would need is 3/4 or just use that 1 in.ply and screw hardibacker