My bathroom floor is constructed as follows from the bottom up
2" X 8" joists 16" on center
3/4" X 7" boards running perpendicular to joists
1/2" x 7" boards running parallel to joists (very wavy)
3/16" plywood?
ceramic tile

Within a few weeks of buying this house the tiles started cracking and
the grout popped out. I just took out most of the tiles by hand.

I was planning to remove the 1/2" boards and put down
5/8" exterior grade plywood
thinset
1/4" Hardibacker
then tile again

The floor will end up a little higher than it is now which is about even
with the hall, but it might still be ok. Would it be better to go down
to the joists and start with 1" ply? If I put thicker plywood on the
joists can I go directly to cement board or are there two layers for a
reason? Is there anything else I should consider? I want to do the job
right and make it last.

Thanks
Dante