Does code require that new sheathing be installed over a 1930’s house that has 1x6 for current sheathing?
Code or not you should sheet over something that old.
can the roof framing handle the extra weight without removing the 1*6?
Codes vary greatly all over the country. And yes a properly built roof should easily support a layer of ply/osb (weighs far less than a 2nd layer of shingles) over the existing 1x6
Code in VA says shingles must be placed on a solidly sheathed surface; no gaps larger then an 1/8". So by code you can get them to pay new decking. Tear off, if youre lucky but an engineer may not back up tear off due to stability of the home.