Adding more weight to a sagging floor system doesn't seem like a great
I own a 1930 house, both bathrooms are tiled with 4" hex over 2x8 joist
w/ ~1' bed.
If / when I repair/ replace, I'll either remove all the tile & bed &
sister to the joists OR I'll just jreplace the cracked tiles.
In your case if the all the sag is in the mddile of the floor, then
probably it's due to deflection of the joists /subfloor because
they're carrying too flexible.
How big is the bathroom? Can you do without for a while?
Since you're going with a new floor, I'd remove all the fixtures & have
at it with an electric demo hammer (Hilti, Bosch, etc).
Check out the joists; remove, replace, sister as needed.
For tile, you want the maximum deflection under a point load (~250lbs)
to be less than the "span" / 360. (This is a minimum criteria usually
applied to the total uniform live & dead loads and usually estimated at
~ 50lbs per sq ft) Tile & backer board can add another 6 psf.
Both the joists AND the subfloor material that spans between joists
have to be checked; the stiffer the better. If it's too flexible, the
tile will crack just like before. TIle placed over "older" wood floor
systems typically crack. :(